"Mathematics / Statistics" Essays

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Mathematical Modeling Term Paper

Term Paper  |  4 pages (1,320 words)
Bibliography Sources: 1+

SAMPLE TEXT:

¶ … Mathematical Modeling

Although even complex mathematical modeling is certainly not new, the process has been facilitated enormously in recent years by the introduction of computer-based modeling applications. Despite these innovations, there are still some significant limitations to mathematical modeling that must be taken into account when using these techniques. To gain some additional insights in this area, this paper provides a review of the relevant literature to identify the benefits and limitations of mathematical modeling, a discussion concerning the use of mathematical modeling in the author's profession and the extent to which such modeling is used as value-added to other kinds of empirical research, and the extent to which it is used in place of other kinds of empirical research. A summary of the research and important findings are presented in the conclusion.

Review and Analysis

Serious interest in mathematical modeling emerged during the mid-20th century when computer science was in its infancy but the need for ways to simulate real-world situations became pronounced. According to Maxwell (2004), "The federal government and many private enterprises have used mathematical modeling since the late 1950s as aids in developing policies, conducting research and development, and engineering complex systems" (p. 67). Today, computer-driven mathematical modeling applications have a number of real-world applications, including gambling and sports simulations as well as modeling human interactions for couples therapy and other "people prediction" applications (Albert, 2002). In this regard, Oliver and Myers report that, "Game theory provides a rich history of considering the strategies derived from various payoff structures, rules about repeating the game, and how players communicate" (p. 34). Mathematical modeling has proven efficacy in other settings as well, including the entire range of economic analyses (Oliver & Myers, n.d.) and even enormously complex weather prediction applications (Kirlik, 2006). Moreover, mathematical modeling has been used to good effect in helping researchers better understand how physiological processes operate at the molecular level. For example, Peter (2008) reports that, "Mathematical models allow researchers to investigate how complex regulatory processes are connected and how disruptions of these processes may contribute to the development of disease" (p. 49).

Furthermore, mathematical modeling can facilitate the systematic analyses of various "what-if"-type scenarios (Oliver & Myers, n.d.), formulate new hypotheses to serve as the basis for regimens of therapeutic interventions and even to evaluate the appropriateness of specific molecules for therapeutic purposes (Peter, 2008). According to Peter, "Numerous mathematical methods have been developed to address different categories of biological processes, such as metabolic processes or signaling and regulatory pathways. Today, modeling approaches are essential for biologists, enabling them to analyze complex physiological processes, as well as for the pharmaceutical industry, as a means for supporting drug discovery and development programs" (2008, p. 50). In fact, some authorities suggest that the limits of mathematical modeling are fundamentally human-based rather than technologically restricted. In this regard, Maxwell (2004) points out that, "Mathematical modeling and computer simulation are limited only by the ingenuity of the person or team conducting the analysis. They have… [read more]


Job Satisfaction Survey Research Studies Term Paper

Term Paper  |  2 pages (580 words)
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Job Satisfaction Survey

Research studies, whether they are clinical trial based, experimental, case study designed, or descriptive, must exhibit and command interest, enthusiasm, and passionate commitment. The research investigator must catch the essential quality of the excitement of discovery that comes from research well done if expected results are to be gained. To this end the researcher is bound by a very stringent protocol for the development of all research endeavors. Not only must the investigator clearly define the research problem but must also plainly state a research question, followed by a testable research null hypothesis. Contained within the format of the research purpose, question, and hypothesis are various inherent constraints that will alert the reader as to the investigator's knowledge of, and adherence to, those tenets that make for sound, credible, and purposeful research (Ohlson, 1998). Included in the aforementioned three research requirements are statements of, and a rational for the use of, specifically chosen variables (independent and dependent), measurement or data assessment tools, statistical data analysis techniques, and potential error sources. Wherein most research fails to deliver scientific information for the advancement of content knowledge is in the area of study error. The remainder of this report will examine one source of possible error, namely that associated with sampling. Once sampling theory has been examined the garnered information will be applied to a specific study using a job satisfaction survey.

Sampling. The most succinct and effective way to view research sampling is to look at the process as being a part of a whole that represents a larger connection (Ohlson, 1998). Briefly defined sampling is the taking any portion of a population or universe, as representative of that population or universe. Sampling alone can skew testing results, infuse…… [read more]


Java Application (Parking Simulator) Interface Description Form Term Paper

Term Paper  |  3 pages (749 words)
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Java Application (parking Simulator)

Interface description

Form

When user launches the application the form1 appears. From form1 we can go to parking form by clicking on "Park." Actions of "Park" button will be viewed later. By the use of panel menu we can do the following:

File-exit - exits the application

Change statistics->Coins available- calls from2 that shows coins available in parking machine

Clicking on button "OK" returns user to Change statistics->Add funds calls form3 that allows to add funds to the machine

Form

Clicking "OK" button adds funds inputted into the machine and return the user to the form1. In order to change the available funds user can view menu Change statistics->Coins available;

Change statistics->General statistics

About-> contains information about the program's

Form4

By clicking on park button on form1 user gets to the form4 which shows parking actions. Here the driver has to choose number of hours and pay for them. He can view the indicator of current time and ending time of parking for which he is supposed to pay. Also the form shows the amount that has to be paid and the amount the driver had already paid. If user makes a mistake in inputting data either for parking time or for amount paid he can cancel payment and will be returned to the form1. In the upper section of the window there are coins of different value for parking payment. By clicking on these coins user will pay corresponding amount of money for parking. When payment is complete buttons become unavailable- user can not add any more money. After the payment is complete and user had paid more than it is supposed, he will get a change menu message form5.

Form5.

On the change menu he can choose the way he want to get change in different variants. He can also watch the change available. After he chooses the variant of payment the program checks for available funds and if the funds are unavailable program gives an error message-Form6

Form6

Then the application returns user to form1.

The data about parking payments can be viewed from report file or in the menu: Change statistics->General statistics Form7

Form7

Information about payments is saved into dynamically creating file Report.txt for future…… [read more]


Pre-Post Test Knowledge of Ultrasound Content Term Paper

Term Paper  |  2 pages (516 words)
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Pre-Post Test Knowledge of Ultrasound Content Knowledge for Sonographers

When an investigative research study ins set up on the basis of a pre and post testing situation the investigator is afforded the opportunity not only to determine differences in mean test scores for the before and after criterion but also establish whether or not there exists a relationship between the pre and post test situation. The latter statistical process is known as a correlation study. In addition the investigator is also able, on an individual participant basis, able to determine wherein each individual places with respect to the average scores on a pre-test basis and on a post-test basis in respect to the group average. This calculation is known as a Z Score.

Descriptive Statistics Results

Pre-Test Ability to Detect Abnormalities

Parameter

Value

Mean

SD

SEM

Median

B. Post-Test Ability to Detect Abnormalities

Parameter

Value

Mean

SD

SEM

Median

C. Mean and Median Graphic Presentation of Differences

Between Pre-test and Post-Test Results

Conclusion: On the basis of the raw data (i.e., non-statistical significant difference) there appears to be a slight increase in ultrasound content knowledge as result of individuals participating in the academic course. Whether or not the reported difference is statistically significant is not known from a review of the raw data. In addition, the conclusion can be drawn that the variability of ultrasound knowledge is more variable before the course vs. after the course.

D. Statistical Analysis of Raw Data visa via "t" Test Calculation:

value and statistical significance:

The two-tailed P. value equals 0.0033

By…… [read more]


Development and Application of These Concepts in Real Life Term Paper

Term Paper  |  6 pages (2,649 words)
Bibliography Sources: 1+

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¶ … Real Life

Golden Ratio:

The golden ratio is acknowledged as the divine proportion golden mean, or golden section is represented as a number mostly confronted while considering the ratios of distances in simple geometric diagrams like pentagram, decagon and dodecagon. It is indicated by the symbol 'phi'. The concept 'golden section' was first used by Martin Ohm in… [read more]


Calculus? Calculus Is a Vast Topic Term Paper

Term Paper  |  3 pages (1,264 words)
Bibliography Sources: 1+

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¶ … Calculus? Calculus is a vast topic and it also forms the basic foundation of any calculations that are based on math. Calculus is divided into two branches, one being differential, and the other being integral. Differential calculus deals with the study of the rates of changes that may happen in functions. For example, it teaches how to find the derivative of a particular function when the function is to determine the angle of the slope of a graph, which deals with that function, at a particular point. Integral calculus generally helps the beginner to deals with certain primitive functions, like for example, indefinite integrals, and also for finding, for example, the area under a curve, known as a definite integral. (Quick math, Automatic Math Solution)

In other words, calculus can be defined as a branch of mathematics that pertains to the rates of change. Although its basic roots can be traced back to Ancient Greece and to Ancient China, its actual origins are indicated in the time of Newton and Leibnitz in the seventeenth century. In the modern world, calculus has proved its usefulness time and again, and it is used extensively in many different areas of science. The there ideas of 'limit', 'derivative', and 'integral' are interwoven into the principles of calculus, wherein while derivative indicates the instantaneous rate of change, in comparison to something else, the integral generally indicates the area under its graph, or a sort of total 'over time'. For example, when the derivative of 'height' in respect to its position, is 'slope', then the derivative of 'position' with respect to 'time', is velocity', and when 'velocity' is taken with respect to 'time', then the derivative would be 'acceleration', and so on. As far as integrals are concerned, the area under the graph is taken into consideration, and this means that when the integral of 'slope', in respect to a constant, is 'height', then the integral of 'velocity', up to a constant, 'position', and thereafter, the integral of 'acceleration', with respect to 'time', is 'velocity'. It is quite evident therefore, that derivatives and integrals are inter-related and are also at times, complete opposites. (Preparing for University Calculus: At Atlantic Canadian Universities)

Why is 'calculus' important in today's world? Science today studies many processes that involve change, and since calculus deals with changes, it is very important. (Preparing for University Calculus: At Atlantic Canadian Universities) One particular High School teacher gave her students concrete examples of how calculus can be applied in real life to solve real problems. The links between the physics concepts of position and velocity and acceleration and the totally calculus concepts of function, derivative and anti-derivative were found. (Dosemagen; Schwalbach, 54) Another teacher toot found that when physics is applied to calculus, the problems would be solved easily. When compared to the way in which these students found it difficult to use mathematics for their calculations, and how they preferred to use physics as a better option, it can be seen… [read more]


Why Algebra Term Paper

Term Paper  |  2 pages (477 words)
Bibliography Sources: 1

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Algebra

How Algebra can be used in real Life

Algebra can easily be used in real life, in many of the calculations which we make every day. The most common example I can think of is using algebra in some way to calculate a rate of change. Let's say for example the hypothetical person who has passed his algebra classes with flying colors and has won a job working for the college has been asked to calculate the rate of change in the number of students who will be attending the school and need to take classes in the next ten years. In this matter, one has to take the formula, which just uses x's and y's and change them into something which has meaning, in this case, the people that will be attending the school. Since we know that in this case, the independent variable we are discussing is the number of students coming to school, we can also make the subject a little bit more complex. We know that the variable can increase, increase exponentially, decrease, remain constant, or any of a number of different things.

So in this case let us make the number of students the function x. By just looking at x we cannot tell what it is going to do, it is too unpredictable. We can only give meaning to x by placing it in context to our study. By this we…… [read more]


Hypatia of Alexandria Term Paper

Term Paper  |  4 pages (1,367 words)
Bibliography Sources: 1+

SAMPLE TEXT:

Historian Coffin continues, "She wanted to help her students understand the mathematics she was teaching, so she wrote books that gave explanations that were easier to understand than the original books" (Coffin, 1998, p. 95). She taught many well-known young men of the time, both Christians and pagans, and most found her an excellent teacher, scientist, and philosopher. She had many friends and supporters in Alexandria, but she also had many detractors.

It is important to note that at the time, it was not especially prestigious or even socially wise to be a mathematician. At the time, astrology and mathematics were closely linked, there were many astrologists and numerologists who were considered mathematicians too, and so, the profession came to be seen in a bad light. Hypatia, "The bad currency drove out the good. Reputable astronomers and geometers like Theon and Hypatia got confused in the popular and in the ecclesiastical mind with these fly-by-nights. All were lumped together as 'mathematicians'" (Deakin, 1997). This was a dangerous position at the time, because Christianity was becoming the dominant religion in Egypt and beyond, and many Christians distrusted science and education. Coffin states, "The Romans did not appreciate Greek mathematics and in fact thought it was subversive. The Romans had not been greatly involved in the development of mathematics; hence their mathematicians did not compare favorably to the Greeks" (Coffin, 1998, p. 96). Thus, as Christianity spread throughout the area, Hypatia found herself in a dangerous situation. Many pagans left the city to save themselves, but Hypatia did not.

In addition to her notoriety as a female scholar and philosopher, Hypatia made no secret of the fact she was a pagan who did not believe in Christianity, and this further alienated her from the Christian majority. She made a strong political and religious enemy when she angered Cyril, the Roman Catholic bishop and leader of Alexandria. Cyril was adamantly against pagans and Jews, and issued many sanctions against them during his forty-year reign. Cyril considered Hypatia an enemy, and where there are not actual texts tying him to her death, most historians regard Cyril as the force behind the mob that eventually attacked and killed Hypatia. Some say Cyril made it known there would be a reward for those who killed the woman.

Eventually, Cyril and his supporters did manage to murder Hypatia, and her death was especially grisly. As she rode through the city in a carriage, her enemies overtook her. Another historian states, "She was seized from her carriage and dragged into the Caesareum, the former temple of the imperial cult, which was now the cathedral. There she was stripped and stoned to death with broken roof tiles. Her body was then hacked to pieces and burned" (Russell, 2000, p. 9). Later, legend has it that her remains were scattered all throughout the city as a warning to other pagans and scientists. The year was 415, and Hypatia was anywhere between 40 and 60 years old.

Unfortunately, none of the… [read more]


Euclid -- 323-285 Term Paper

Term Paper  |  4 pages (1,585 words)
Bibliography Sources: 1+

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The cause that such a proof was in great demand for such a long time was due to the fact that Euclid's other postulates seem to be easy, self evident, and naturally clear, the fifth postulate basically described the intersection of lines at potentially infinite distances -- the notion of infinity being at the time, was mathematically, problematic. (Euclid: www.mathdaily.com)

Therefore, the fifth postulate seemed as a sort of blotch in the otherwise apparently perfect logical edifice which is Euclid's Elements. Whereas Elements was referred and used into the 20th century as the original geometry textbook and has been regarded a fine example of the formally precise axiomatic method, Euclid's study fails to meet the modern standards and several logically necessary axioms are not there. The first correct axiomatic treatment of geometry was given by Hilbert during the year 1899. Nearly nothing is available regarding Euclid, apart from what is presented in Elements and some of his other surviving books and whatever scanty biographical information the world has comes mostly from explanations by Proclus and Pappus of Alexandria. (Euclid: www.mathdaily.com)

REFERENCES

Dietz, Elizabeth. "Euclid 323-285 B.C. Biography" Retrieved from http://www.albertson.edu/math/History/edietz/Classical/biography.htm

Accessed on 8 August, 2005

Dietz, Elizabeth. "Euclid 323-285 B.C: Discoveries" Retrieved from http://www.albertson.edu/math/History/edietz/Classical/discoveries.htm

Accessed on 8 August, 2005

"Euclid's Elements" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclid%27s_Elements

Accessed on 8 August, 2005

"Euclidean Geometry" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclidean_geometry

Accessed on 8 August, 2005

"Euclid" Retrieved from http://www.mathdaily.com/lessons/Euclid

Accessed on 8 August, 2005

"Euclid" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclid

Accessed on 8 August, 2005… [read more]


Mathematician Nassar, Sylvia. A Beautiful Mind Term Paper

Term Paper  |  2 pages (638 words)
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¶ … Mathematician

Nassar, Sylvia. A Beautiful Mind. New York: Touchstone Books, 1998.

The story of the 1994 Nobel-Prize winning mathematician and economist John Nash has proved to be an inspiration to all individuals who have heard and read about the great Princeton genius, and not simply because of Nash's ground breaking insights about the mathematics of game theory. Nash is equally famous for his return from his prison of mental illness. He is now once again dwelling in the lucid world of his previous, brilliant mind, in a state of sanity. Author Sylvia Nassar's biography A Beautiful Mind tells the story of how Nash was born in the Ozarks, one of the poorest regions of America. As a young man, he was arrogant yet intellectually talented. After becoming a graduate student at Princeton, he even challenged Albert Einstein face-to face about the older man's theory of relativity. Einstein dismissed the young Nash's concerns from a mathematical point-of-view, but was impressed by Nash's bravado.

Nash became famous as a young man because of his unique insights into game theory, a theory that attempted to rationally predict how human beings made decisions with imperfect information, as people must in certain kinds of games, worldwide diplomacy, and economics. Ironically, although Nash's mathematical theories are used to predict human behavior with numbers and equations, even before he began to lose his reason, Nash had a great deal of difficulty relating to other people, even his fellow mathematicians. One of the reasons Nash loved mathematics was that he did not need to deal with other people's emotions in a world of numbers. According to Nassar's book, even before he developed the symptoms of schizophrenia, his contemporaries, "found him immensely strange," and "aloof." (Nassar, p. 13) Even so, by the 1950s, Nash had carved a brilliant career "at the apex of the mathematics profession, traveled, lectured, taught," and met "the most famous mathematicians of…… [read more]


Proof David Auburn's "Proof" -- Catherine Term Paper

Term Paper  |  2 pages (628 words)
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Proof

David Auburn's "Proof" -- Catherine vs. Claire

How can two sisters from the same family be so different?

Both fulfill different functions and roles in the family dynamic. Catherine is the caretaker, and the mathematical problem-solver. Claire is the problem-solver, in a practical sense.

Temperamentally, Claire takes risks in finance, Catherine hides from the world, locked in her father's reality, and does not embrace risk, only intellectual risks on the Both represent two different aspects of mathematics. Catherine represents mathematics' theoretical side, while Claire's career in finance and concern with money demonstrate the worldly value of numbers

Catherine's characteristics

Compassionate, as manifested by her role in the caretaker of her mathematician father until recently freed by his death

Confined socially, limited professionally, and kept in a childlike state personally by her father's mental illness

Depressive, reluctant to move forward even after a change, pessimistic

Allied with her father, even after he dies -- experiences his presence in a ghostly fashion

Still young in terms of her sexual experience, even though she is in her 20s

Over the course of the play, says she has discovered revolutionary mathematical theory amongst her dead father's papers -- Claire expresses surprise

Protective of father's memory as a great man

Protective also of father emotionally, did not, when he was living, allow him to be fully cognizant of the extend of his illness, while Claire believes she sees her father's illness (and her sister's) clearly However, in doing so, may also have been protecting herself from moving out into the world, which her older sister Claire was able to do much more successfully

Loves father without reservation -- finds her identity in caring for her father, unlike Claire who finds her identity by breaking away from the family and becoming engaged in professional, normal life

Moody, withdrawn, emotionally unstable

Might be author of the supposedly new proof --…… [read more]


Statistical Tests Can Provide More Information Data Analysis Chapter

Data Analysis Chapter  |  1 pages (383 words)
Bibliography Sources: 2

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¶ … statistical tests can provide more information than a single one, allowing for more meaningful assessments of a situation. This interaction of two statistical tests (as described below) demonstrates that in this scenario younger women are by far the most likely to be the best employees for this call center.

The Pearson r provides an answer to the question of whether or not two variables are related to each other. More than simply establishing whether a relationship exists or not, Pearson r determines how strong this relationship is and whether it is a direct or inverse relationship. In a direct relationship, if one variable goes up than so does another (or others).

For example, in general as an individual's height goes up, so does his/or her weight. In an inverse relationship, as one variable goes up another one goes down. An example of this would be: The fewer workers are assigned to construct a building the longer it will take to construct the building. Both of these relationships cited here make intuitive sense to us. We may never have considered them to be a part of the world of statistics,…… [read more]


Database Developer (Based on Job Research Paper

Research Paper  |  2 pages (695 words)
Bibliography Sources: 0

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I instructed the optimizer to use a specific access path by using a hint.

d. Access Plan Execution

-- Executes the selected access plan.

I used the EXPLAIN PLAN command for looking at the execution plan of the SQL.

2. Provide examples of errors that you had during your professional experiences.

I had been frustrated with questions that included the following: why the query was running slow; why one query was going slower than another; I wondered whether my index was getting used, and if not, why not... The execution plan told me how the query would be executed, but I had trouble following the steps and had to be habituated to it. Syntactic analysis took a while.

As novitiate, I had difficulty in the beginning reading the code (in the results of the query) as well as understanding the different graphical, text and XML execution plans. The Graphical Plans were somewhat easier to read than the Text Plans, although the detailed data (of graph) was somewhat harder. The format that may have been the most obscure for me was the SHOWPLAN_TEXT

I had also been advised to do certain things for querying and working with the plan cache. I had to run a certain SQL script in order to see how long a plan takes to compile. In the beginning, I had to ask someone in order to understand the objects within the cache (in order to see how the optimizer and storage engine created my plan).

There were also differences between the esti-mated and actual execution plans. This probably occurred due to statistics being stale when over time data was modified and the statistics gradually became mismatched to actual data. I was told that I received bad execution plans because the statistical data was not up-to-date.

Sometimes, when I wanted a parallel query, I saw a completely different plan -- simply because the optimizer felt it could not support my request at that time. At least once or twice the estimated plan didn't work at all since it…… [read more]


Offline During the Final Exam Week A-Level Coursework

A-Level Coursework  |  7 pages (2,030 words)
Style: APA  |  Bibliography Sources: 7

SAMPLE TEXT:

¶ … offline during the final exam week. Once you have complete the exam, input your exam into the final exam shell in the exam folder on the course web-page. Good luck

Census statistics show that college graduates make more than $254,000 more in their lifetime than non-college graduates. If you were to question the validity of this observation, what… [read more]


Norway Brand Statistical Summary and Hypotheses Decisions Data Analysis Chapter

Data Analysis Chapter  |  5 pages (1,712 words)
Bibliography Sources: 0

SAMPLE TEXT:

Norway Brand

Statistical Summary and Hypotheses Decisions

The statistical method used to compare the experimental group to the control group was straightforward and fairly standard. First, with an established confidence interval of 95% and a significance or alpha of .05, the Critical't score for the control group was established using Excel's built-in function. For each instrument item compared, the mean,… [read more]


Speeches and Presentations Essay

Essay  |  2 pages (677 words)
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Speech Organization

When a presentation is made there are certain verbal and visual supports that can be used to aid it. This supports are quite important in that they help in clarity as they make ideas that are complicated clear. They also help in developing interest in the audience as they make the main points more vivid. Finally this supports make the presentation more convincing because they provide evidence that enhance the claims made. This paper will therefore look into these supports and the impact they had on a presentation that I attended. Verbal supports include definitions, examples, stories, statistics, comparisons, quotations, citing sources and so on. On the other hand the visual supports include objects, diagrams, list and tables, photographs and so on.

What captured my interest in the presentation?

The verbal support that captured my interest in the presentation is the use of "Examples." I really liked the way the use of examples has been used in the presentation was. This helped me as the audience in understanding well what the presentations were all about. The brief illustrations of the points allowed me to get exactly what the presenter was talking about and it became very effective since several of the examples were given out.

What confused in the presentation

The use of statistics really confused me. This is because there were many numbers that the speaker used to present their ideas. The choice of the statistics that was applied and hence the statistics presented were very overwhelming to me. Another verbal support that confused me was the use of comparisons. This is because I did not seem to clearly get the figurative analogies that were being applied. They were very confusing to me since I could not seem to get the validity of the comparisons that were being made.

What bored me in the presentation

What made me bored in the presentation was in the way the stories were narrated. For instance, the stories given was non-fiction, hence did not create materials that helps the…… [read more]


Random Variable for Each Statement as Being Term Paper

Term Paper  |  3 pages (820 words)
Bibliography Sources: 3

SAMPLE TEXT:

¶ … Random Variable for Each Statement as Being Discreet or Continuous by

(a) the number of freshman in the required course, English 101

A) Discreet B) Continuous

(b) the number of phone calls between Florida and New York on Thanksgiving day.

A) Discreet B) Continuous

(c) the height of a radomly selected student.

A) Discreet B) Continuous

(d) the number of spills that occur in a local hospital.

A) Discreet B) Continuous

(e) the braking time of a car.

A) Discreet B) Continuous

Provide an appropriate response.

List the four requirements for a binomial distribution.

(i) Observations are independent

(ii) Outcome of observation is either a success or failure

(iii) Probability of outcome is the same

(iii) Fixed number of observations

Identify each of the variables in the binomial probability formula.

P (x) = __ n!__ . px . qn-x

(n -- x)! x!

n = number of trials x = number of successes p = probability of success q = probability of failure

Also, explain what the fraction __ n!____ computes.

(n -- x)!x!

Number of ways to select 'x' items from 'n' given items

4. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

n = 12, x = 5, p = 0.25, q = 0.75

P (x = 5) = __ 12!__ . (0.25)5 . (0.75)(12-5)

(12 -- 5)! 5!

= __ 12!__ . (0.25)5 . (0.75)7

7! 5!

= 12 x 11 x 10 x 9 x 8 x 7!_ . (0.000977). (0.133484)

7! x 5 x 4 x 3 x 2 x 1

= 0.103241

CHAPTER 6

1. The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Test on a large sample of these instruments reveal that at the freezing point of water, some thermometers give reading below 0° (denoted by negative numbers ). Assume that the mean reading is 0°C and that standard deviation of the reading is 1.00°C. Also assume that the readings are normally distributed. If one thermometer is randomly selected the, find the probability that at the freezing point of water, the reading is less than 1.57°C.

Z-score

Area

1.5 + 0.07 = 1.57

0.9418

This is already standardized,

2. If Z. is the standard variable, find the probability, that Z.…… [read more]


ANOVA Study Analysis of Variance Research Paper

Research Paper  |  3 pages (774 words)
Bibliography Sources: 2

SAMPLE TEXT:

Alternative Hypothesis: There is no significant difference between the treatments that the students are subjected to.

Assumptions:

It is important to note here that in this case, there are two assumptions that will be made;

1. That there is a normal population distribution.

2. The variance associated with each variable is the same.

Types of errors likely in ANOVA case

Accuracy in statistics is the degree of closeness of a measurement of a quantity to the quantities true or actual value. Precision also termed as the reproducibility or repeatability is the degree to which repeated measurements under conditions that are not changed. A measurement in a system can be accurate but not precise and also accurate but not precise; it can also be neither or both. There are two categories of errors therefore experienced frequently in such a calculation. Type I and type II errors. Type I error is also known as error of the first kind and it occurs when the null hypothesis is true but is rejected. Type II error is also known as the error of the second kind and occurs when the null hypothesis is false but is not rejected erroneously. An example of the relationship between accuracy and precision if for instance when one reads out time right to the second even if one knows very well that the watch they are reading from is one minute slow, this means that the reading is precise but it is not accurate. An example of the relationship between type 1 and type 2 errors in our case would be that the type of treatment that the students are subjected does affect their marks. Type I error occurs when a conclusion is made that the treatment does not affect the performance in GMAT when it actually does. While a type II error is made when a conclusion is made that the treatment does affect the performance while it actually does not (Shera, 2006). In short, Type I is when the null hypothesis is rejected yet it should not and Type two is when the null hypothesis is accepted yet it should not be accepted.

References

Shera, J (2006). Statistical Errors (Type I, Type II,…… [read more]


Criminal Justice and Criminology Interpreting Simple Data Research Proposal

Research Proposal  |  7 pages (2,030 words)
Bibliography Sources: 6

SAMPLE TEXT:

¶ … Criminal Justice and Criminology

Interpreting simple data

The data collection exercise involved posting a picture of a bear on Facebook. The caption of the picture asked viewers to provide their thoughts on the picture. This caption was kept simple in order to prevent bias that could arise from asking viewers to like or dislike the pictures. The data… [read more]


Forensics One of the Most Important Statistical Discussion and Results Chapter

Discussion and Results Chapter  |  2 pages (522 words)
Bibliography Sources: 2

SAMPLE TEXT:

¶ … Forensics

One of the most important statistical concept that deals with psychological research is the population being studied. Although it may sound preliminary, deciding who to be studied is the most primary, and thus important, subjects in all of research. Specifically, for psychological research, population selection dictates the basis of many of the subjects involved. In something as subtle and imprecise as psychology, the population the research is selected from is that much more important.

Another statistical idea that is of great importance is the relationship between validity and reliability. Once again, subtle and nuanced definitions of these words help create arguments that become documented and eventually known as facts. Understanding the difference and important of each of these terms can also explain misunderstandings that occur in seemingly well thought out experiments and research. Either way, both concepts can lead to learning and improvement, each in their own way.

Some other statistical ideas are very interesting. One such idea is the ability to predict the future with statistical inference. Although nothing is guaranteed in life, through mathematical relationships, statistics can help create images of the future in predictive and systematic ways. This discovery is truly overlooked in many instances, and in others, too heavily relied on. Finding a balanced and reasoned approach to the incorporation of statistical inference to science remains an interesting challenge.

Dunifon (2005) raised another interesting point in dealing with statistical concepts. He wrote that "experiment is the only way to truly determine whether a treatment causes an outcome." I agree with this very interesting concept,…… [read more]


Russia's Contributions to Science Essay

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Russia's Contribution To Science

Russian contribution to the field of science is famous due to many reasons including the invention of Radio by a. Popov, development of the periodic table by D. Mendeleev, the creation of principals in relation to the space flights, which are interplanetary, on multistage rockets by K. Tsiolkovskiy. The Russian scientists contributed a lot to the… [read more]


Teach Geometry Dear Parent Essay

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Children develop their math vocabulary and learn to use appropriate terms. They have an opportunity to connect new understanding to prior knowledge. Math is not simply rote learning of facts and equations. The Common Core State Standards (CCSS), already adopted by forty-five states, were designed to facilitate higher-order thinking and problem solving skills ("Common core standards adoption by state," 2012). These abilities will better prepare students for the real world. Students will communicate with their teachers and with their peers to figure out different ways to solve problems. There is focus on problem solving as a process, so students will be able to understand where they went wrong and so they will be able to solve similar problems in the future.

As far as studying geometry instead of "the basics," geometry is the basis for much of what we do in mathematics. The foundations young students will get in geometry will support their work later on in higher-level mathematics. For example, fractional amounts and percentages are most often represented using geometric shapes. Shapes drawn on a coordinate grid are analyzed in terms of algebraic relationships. Geometry can be thought of as "a conceptual glue" (Schwartz, 2008, p. 72) that connects many different areas within mathematics. With respect to real-world applications, analysis of two- and three-dimensional shapes and the study of geometric relationships are used in fields such as landscaping and architectural design. The ability to specify locations and describe spatial relationships is necessary in transportation, navigation, and construction. Transformations and symmetry are useful in packaging and product design, as well as artistic expression. Geometry made possible the programming of computer graphics and the intuitive interface with computers (Schwartz, p. 72).

Your child's teacher

References

Chard, D.J., Baker, S.K., Clarke, B., Jungjohann, K., Davis, K., and Smolkowski, K. (2008).

Preventing early mathematics difficulties: The feasibility of a rigorous kindergarten mathematics curriculum. Learning Disability Quarterly 31(1), pp. 11-20.

Common core standards adoption by state. (2012). ASCD. Retrieved from http://www.ascd.org/common-core-state-standards/common-core-state-standards- adoption-map.aspx

Cooke, B.D., and Buccholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal 32(6), pp. 365-369).

Schwartz, J.E. (2008). Elementary…… [read more]


Calculus and Definitions Assessment

Assessment  |  5 pages (1,309 words)
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In simple terms the Riemann sum is used to define the definite integral of a function. We begin by considering a simple case, whereby the definition of the Riemann integral of a continuous function f over a rectangle R. In this case rather than having a one-variable case, we can overcome the tendency of connecting integration too strongly with anti-differentiation. (Buck 2003)

Formal definition

It is the definition of a function by use of graphs to define the limits; it uses Greek letters epsilon (?) and Delta (?). Epsilon always represents any distance on the limiting side and delta represents the distance on the x- axis. The limits of a given function clearly explain how that given function behaves when it nears the x value.

Consider the following functions g (x) and f (x), this functions are as a result of definition of real numbers. The following relationship exist x ?

This relationship exist only when there is a positive constant C. such that for all sufficiently large values of x, f (x) is at most C. multiplied by g (x) in absolute value. That is, f (x) = O (g (x)) if and only if there exists a positive real number C. And a real number x0 such that

In general the growth rate are of much interest in that the variable x which goes to infinity is often left unstated, and one writes more simply that f (x) = O (g (x)).

Additional explanation indicates that it doesn't matter how close a function can be to a limit, it is always necessary to find the corresponding x value which is closer to the given value and using the new notations of epsilon (?) and delta (?), we make f (x) within ? Of L, the limit, and later determine x within ? Of C. (Bradley et al.,.2000)

Again, since this is tricky, let's resume our example from before: f (x) =x2at x=2. To start, let's say we want f (x) to be within .01 of the limit. We know by now that the limit should be 4, so we say: for ?= 0.1, there is some ? so that as long as, then

To show this, we can pick any delta (?) that is bigger than 0, so long as it works. For example, you might pick .000000001, because you are absolutely sure that if x is within .00000000000001 of 2, then f (x) will be within .01 of 4. This works for. But we can't just pick a specific value for, like .01, because we said in our definition "for every." This means that we need to be able to show an infinite number of s, one for each.

In summary indefinite integration exists when the limits of integration are not given, this means that the upper and the lower limits are not given. Definite integration occurs when the limits are given and therefore you need to calculate the area that is when x=c to x=d

Examples… [read more]


Score Z Scores Z Research Proposal

Research Proposal  |  1 pages (351 words)
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33

P= Area of the curve beyond 1.33

=0.0918 or 9.18%

b) Less than 80 minutes

Using formula Z=X-? + ?

Z=50-60/15

=10/15

=-0.67

P= Area of the curve below -0.67

P=0.2514

%=25.14%

Between 45-75

Using the formula Z=X-? + ?

Z (45) =45-60/15

=-1

Z (75) = 75-60/15

=1

P between -1 and 1

= 0.3413 + 0.3413

=0.6826

% =68.26%

Question 3

Bob takes an online IQ test and finds that his IQ according to the test is 134. Assuming that the mean IQ is 100, the standard deviation is 15, and the distribution of IQ scores is normal, what proportion of the population would score higher than Bob? Lower than Bob?

Proportion higher than Bob would be the area of the curve beyond Bob's score, the proportion lower than Bob would be the area of the curve below Bob's score.

Using the formula Z=X-? + ?

Z =134-100/15

=34/15

=2.27

P Higher than Bob's Score = 0.0116

P Lower than Bob's Score =0.9984

References…… [read more]


Bayes Probability Can Bayes Confirmation Essay

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[footnoteRef:7] He was studying the paradox which arises from the use of Bayes theorem when trying to explain phenomena in the field of psychology. He states that; [7: PE Meehl, 'Theory-testing in psychology and physics: A methodological paradox', Philosophy of Science, vol. 34, 1967, pp. 103-115.]

'In the physical sciences [physics, and others], the usual result in an improvement in… [read more]


Nursing Research: Discussion Questions Quantitative Essay

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The human rights of subjects must always be protected in research -- and that includes not publishing data that could result in harm to individuals, who are treated in a particular manner, based upon inaccurate data.

Q4. A simple hypothesis states the relationship between two variables. A complex hypothesis states the relationship between three or more variables. A nondirectional hypothesis states that a relationship exists between two variables. A directional hypothesis predicts the relationship between the two variables (Burns 2010: 172-173). An associative hypothesis describes phenomenon that occur together, while causal hypothesis describes one phenomenon that causes another (Burns 2010: 168). A null hypothesis states that there is no relationship between two variables (and usually the researcher wants to disprove the null hypothesis). The research hypothesis states that there is a relationship between the two variables, which the researcher is usually trying to prove.

Q5. Quantitative research attempts to accumulate numerical data about a specific phenomenon. A quantitative literature review attempts to accumulate data from a vast array of different quantitative studies, to either describe or find out specific tendencies in the types of hypotheses tested regarding the phenomenon. Of course, it is rare that all studies will reach the same conclusion, so the researchers will evaluate the quality of the studies (for example, if a study produces an anomalous result, the author of the review will likely try to determine why this is the case, such as if there was too small a sampling size). The literature review may reach a conclusion about the phenomenon, based upon statistically analyzing the data. A qualitative research study merely assesses the variety of informational studies on a particular phenomenon to paint a clearer picture of…… [read more]


Derivatives and Definite Integrals Word Term Paper

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This is done with a "time derivative" which defines the rate of change over time. The instantaneous velocity of an object is calculated by the coordinate derivative relative to time. To know how quickly the velocity of a given object will change in the course of time, another value called acceleration is defined. Thus, acceleration is the time-derivative of an object's velocity.

How are derivatives used to solve maximum and minimum problems? The maxima and the minima, also known as the extremum, are the values of the largest and smallest limits that a function may take in a given point. They are expressed as a set of greatest and least values. Derivatives are used to determine these points. The derivative of a function is interpreted geometrically as the slope of the curve of the mathematical function y (t), whereas the function of t is plotted. The derivative is noted as positive when a function increases toward a maximum; the maximum being horizontal at zero. It is considered negative just beyond the maximum. The second derivative notates the rate of change. It is called negative since the process of the slope, as described, is always getting smaller. The second derivative is always negative and corresponds to a maximum.

How is the definite integral used to solve area problems? A definite integral is an integral with upper and lower limits. It is used to calculate the area of certain regions in the plane. In the calculation of the area of a region, the region finds a limit above by the graph of a function f (x), below by the x -axis, and on two sides by vertical lines that correspond to the equations x = a and x = b.

References

Nave, R. Derivatives and integrals. Hyper Physics, Retrieved from http://hyperphysics.phy-astr.gsu.edu

Kouba, D.A. The Calculus Page, U.C. Davis Department of Mathematics. http://www.math.ucdavis.edu, Retrieved January 25, 2011

Weisstein, E. Wolfram Mathworld. http://mathworld.wolfram.com, Retrieved January 25, 2011… [read more]


Dot Maps of Three Datasets Term Paper

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In the same figure, pine tree data points are randomly distributed in grids. The distribution density changes by changing the size of quadrat area (see Figure 5). For example, 8th and 13th quadrats of redwood data exhibit the highest density of data points whereas 1st, 6th and 14th quadrats do not contain any data point.

In order to test the CRS hypothesis, the appropriate quadrat counts were visually investigated (see Figure 2, 3, and 6. Eventually, the grid size is chosen as 10x10. The mean value, variance, standard deviation and VMR for each dataset were calculated by using MATLAB scripts (i.e., mean, var, std). The results are shown in table 3.

Table 3. Mean, variance, standard deviation and VMR values calculated for 10x10 quadrats.

Cell

Redwood

Pine

Mean

0.42

0.62

0.65

Variance

0.25

1.39

0.61

STD

0.50

1.18

0.78

VMR

0.59

2.24

0.94

The mean values of Redwood and pine datasets are similar; however, it was already analyzed that these two datasets show different distribution characteristics. Variance (square of standard deviation) is another value used to describe the distribution of datasets. Since the variance provides the information about the relative distance between mean and data point, one could say that the cell data is the most uniform data within analyzed datasets. The last value calculated in table 3 is the variance mean ratio (VMR). This ratio of the variance value to the mean value is used to identify whether the dataset is dispersed or clustered compared to CSR hypothesis. Finally, VMR value would quantify the distribution model of any dataset. The VMR value for Poisson distribution is defined as 1.The negative binomial distribution requires a VMR value larger than 1 while binomial distribution has a VMR value smaller than 1. In this regard, the cell and the pine datasets are under-dispersed. In other words, the data points are distributed uniformly in the spatial domain. Therefore, these two datasets obey the definition of binomial distribution. The redwood data is over-dispersed meaning the data points are clustered together. Thus, the underlying distribution model for redwood is negative binomial distribution.

Taken all together, one can define the distribution models of the datasets; however, the relationship between individual data points cannot be discussed only by quadrat count method.

Figure 6. 25x25 Grid.

To validate a null hypothesis the z-scores of three datasets is calculated using CrimeStat-III. The criteria for z scores (95% confident) are as follows.

(1) Region of significance (rejection of the hypothesis) if the set of z scores is outside of the range -1.96 to 1.96

(2) Region of non-significance (acceptance of the hypothesis )if the set…… [read more]


Statistical Research II Measuring Research Paper

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The Median is the number in a set that equates to the middle, if every figure in the distribution were to be listed in ascending or descending order. One of the most attractive aspects of the median from a statistical analysis standpoint comes from the fact that "the median is often used instead of the mean for asymmetric data because it is closer to the mode and is insensitive to extreme values in the sample" (Bickel, 2003), and this ability to resist the effects of variant data makes the median an extremely effective diagnostic tool. Median can also be conceptualized as the exact point within a number set where perfect separation into two halves occurs, with exactly 50% of the values in the distribution falling to one side or another, which is why statisticians often refer to the median as the visual center of a numerical distribution.

Crude Range is the result of subtracting the lowest number in a distribution from the highest. The Range equates to the amount of distinct values which are present between these highest and the lowest data points, when one includes the highest and lowest values that are present. The most prevalent limiting factor linked to the application of crude range and range is based on these tools being so reliant on the extreme ends of a distribution set, which typically complicates most analytic processes with the presence of variance. When one refers to the standard deviation, this term describes the precise level of variation or dispersion from the mean that can be detected. When the standard deviation is a low number, this is reflective of data points that are closely situated to the mean, while on the other hand standard deviations that are high numbers are derived from data points that span a wide spectrum.

References

Bickel, D.R. (2003). Robust and efficient estimation of the mode of continuous data: The mode as a viable measure of central tendency. Journal of statistical computation and simulation, 73(12), 899-912.

Manikandan, S. (2011). Measures of…… [read more]


Georg Cantor: A Genius Out Term Paper

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Cantor's most criticized concept presented in this paper is that the power of the continuum is independent from its number of dimensions. It was commonly believed that points in two dimensional space cannot be traced back to one dimensional space, and Cantor had thought that he could get higher transfinite powers by going from the one-dimensional to the multi-dimensional. Here… [read more]


Fractal Geometry Term Paper

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His mind was a visual one, a geometric mind, yet he was not taught this way.

Mandelbrot claims he could not do algebra well yet managed to receive the highest grades by translating the questions mentally into pictures. When he finished school, he came to the United States, where IBM gave him the freedom to pursue his mathematical interests, as he deemed worthy.

Mandelbrot's research led to a huge breakthrough summarized by a simple mathematical formula: z -> z^2 + c. This formula is now called the Mandelbrot set. It is important to understand that this formula, and the Law of Wisdom which it represents, could not have been discovered without computers. Many say that this mathematical breakthrough, which occurred in the research laboratories of I.B.M., is the greatest in twentieth century mathematics.

The Mandelbrot set is a dynamic calculation based on the iteration of complex numbers with zero at the beginning. The order behind the chaotic production of numbers created by the formula can only be seen by the computer calculation and graphic portrayal of these numbers on computers. Otherwise the formula appears to generate a totally random and meaningless set of numbers. It is only when millions of calculations are mechanically performed and plotted on a computer screen that the hidden geometric order of the Mandelbrot set is seen. The order is of a beautiful yet different kind, containing self-similar recursiveness over an infinite scale.

Euclidian geometry was unable to describe the shape of a cloud, coastline, a hill or a tree. As Mandelbrot says in his book the Fractal Geometry of Nature:

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

Mandelbrot broke the long-term chain of thinking that held that most of nature's systems were too complex and strange to be described in mathematical terms. Fractal geometry opened a new world of mathematics that is capable of describing mathematically the most strange and complicated forms of the real world. In Mandelbrot words: "Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently."

The Mandelbrot set has done much more than just produce beautiful pictures. When pictures are thoroughly examined, innumerable empirical observations are found that can be restated in the form of mathematical conjectures. Many of these have already led to brilliant theorems and proofs. Fractal geometry has inspired a new approach to mathematics, using a computer screen.

The discovery simply started a new way of thinking, which will undoubtedly change the way many things in the world work. Fractal geometry is opening doors to significant new insights into complex phenomena, including cells, hearts, brains, coastlines, mountains, earthquakes, economies, political systems, art, music, climate & life.

Bibliography

Mandelbrot, Benoit B. The Fractal Geometry of Nature W.H. Freeman and Company, 1977.

Crilly, R.A. Fractals and Chaos. Springer-Verlag, 1991.

Dictionary of Scientists, Oxford University Press, Market House Books Ltd., 1999… [read more]


Euclid's Fifth Postulate Philosophical Term Paper

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Whether the fifth postulate is true or false also affects the kind of geometry that is being used. For example, if the postulate is true, than Euclidian geometry works. If the postulate is false, then it creates a non-Euclidian type of geometry where similar triangles must always be congruent and the Pythagorean Theorem is no longer valid (Bennett, 2000).

Whether Euclid's fifth postulate is true, false, or both, it will continue to be debated by scholars and mathematicians for many years to come. Whether it will ever be 'solved' or proved remains to be seen. Either way, it is a fascinating and problematic piece of information that will carry on Euclid's legacy for centuries. If someday it is proven to be either true or false, and the decision is agreed upon, then it could change the way mathematics are done and the way geometry is looked at during the present time and also well into the future. Euclid would have likely enjoyed the attention his simple thoughts are receiving.

Works Cited

Bennett, Andrew G. The Axiomatic Method. 2000. Math 572 Home. 2 December 2002. http://www.math.ksu.edu/math572/notes/824.html.

Bogomolny, Alexander. The fifth postulate: attempts to prove. 2002. Cut the Knot. 2 December 2002. http://www.cut-the-knot.com/triangle/pythpar/Attempts.shtml.

Parallel lines and planes. 2002. Connecting Geometry. 2 December 2002. http://www.k12.hi.us/~csanders/ch_07Parallels.html.… [read more]


Isaac Newton Was the Greatest Term Paper

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Newton's three laws of motion explained the hitherto inexplicable behavior of all physical bodies in motion. Still more astounding was Newton's discovery of gravity. All these four laws put together explained the mechanical motion of all earthly and heavenly bodies. Newton not only proposed these laws but also ratified them by using the integral calculus.

Newton published his laws of motion and gravity in his famed work 'Mathematical Principles of Natural Philosophy' (Principia) in 1687. [Microsoft Encarta] Newton's revolutionary discoveries were applied to a wide array of subjects. The field of Astronomy in particular got a tremendous impetus from his laws of motion. Using these laws Newton was able to precisely identify and predict the position of planets and other heavenly bodies. This was a significant milestone in the field of astronomy and for this reason Newton is rightly regarded by many as the greatest of all astronomers.

As for Newton's accomplishments we can do better by quoting some of the other great scientists. The great French scientist Laplace said, " The Principia is preeminent above any other production of human genius." Lagrange, another famous mathematician opined that Newton was the greatest genius who ever lived. Ernst Mach on his part said "All that has been accomplished in mathematics since his day has been a deductive, formal, and mathematical development of mechanics on the basis of Newton's laws." [Michael.H. Hart]. In conclusion we can say that in the history of science Newton's name is indelibly imprinted and perhaps his laws and discoveries are the most referenced by the scientific world. It is clear that Newton is not only one of the greatest scientists but also one of the most influential scientific personalities.

Bibliography

Michael.H. Hart, "The 100, A Ranking of the Most influential Persons in History"

Isaac Newton', 1999, Meeraa publications.

Microsoft Encarta, "Isaac Newton," Accessed on 2nd, December 2002, http://www.newton.cam.ac.uk/newtlife.html

D.R.Wilkins, "Sir Isaac Newton (1642-1727)," Accessed on 2nd, 2002

http://www.maths.tcd.ie/pub/HistMath/People/Newton/RouseBall/RB_Newton.html… [read more]


Lives of Archimedes and Carl Term Paper

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The Latin translation influenced the work of the foremost mathematicians and physicists of the time, including Johannes Kepler and Galileo. A 1615 Latin translation of his complete works, was enormously influential in the work of Rene Descartes and Pierre de Fermat. The mathematical advances in Europe from 1550 to 1650 was build largely on the work of the ancient mathematicians, especially Archimedes ("Archimedes").

In contrast, Gauss's work had immediate impact on both theoretical and applied mathematics. This was partly because Gauss himself was interested in the applications of his work. Gauss also lived during the dawn of the Industrial Age, a time of unprecedented scientific advancement.

Gauss's interest in gravitation and magnetism led to a published paper in 1840 on real analysis. This paper became the starting point for the modern theory of potential. In the beginning of the 20th century, mathematicians re-developed potential theory, on the basis of Gauss's initial conclusions. In 1830, Gauss's mathematical investigations of fluids at rest contributed to the development of the Law of Conservation of Energy. His collaborative work with William Weber on electromagnetism paved the way for the invention of the telegraph. In addition to electromagnetism, Gauss's works in algebra and numbers theory continues to have significant impact on current mathematical research, including geometry and modern telecommunications ("Gauss").

Conclusion

In conclusion, the work of Archimedes and Gauss continues to make significant contributions to all fields of mathematics. Many mathematical disciplines would not even be possible without their work.

Both men faced significant obstacles to their mathematical research. Archimedes lived in a time of very limited mathematical knowledge. Even commonplace mathematical concepts today - the ideas of the infinitesimal, pi, and infinity - were unheard of during his time. The cumbersome Greek and Roman numeral systems were unwieldy for his computational needs so he had to devise his own.

Gauss, on the other hand, was born into poverty and did not have his family's support. He lived in or close to poverty for much of his life.

However, both men eventually overcame these obstacles to produce their research. Centuries after their deaths, the work of these two great minds continues to revolutionize the science of mathematics.

Works Cited

Archimedes," in Guide to the History of Calculus. Retrieved 30 November 2002 from http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/bios/archimedes.htm

Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare. New York and London: Simon and Schuster, 1965.

Boyer, Carl B. A History of Mathematics, 2nd ed. New York: John Wiley and Sons, 1991.

Gauss," in Guide to the History of Calculus. Retrieved 30 November 2002 from http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/bios/gauss.htm

Muir, Jane. Of Men and Numbers: The Story of the Great Mathematicians. New York: Dover Publications, 1996.

Riley, Mark T. "Archimedes"…… [read more]


Structure the Research Term Paper

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Individual researchers must monitor a vast number of research results and activities that have a bearing on their own particular specialties.

By definition, measurement must be objective, quantitative and statistically valid. Simply put, it's about numbers, objective hard data. A scientifically calculated sample of people from a population is asked a set of questions on a survey to determine the frequency and percentage of their responses. For example: 240 people, 79%, of a sample population, said they are more confident of their personal future today than they were a year ago. Because the sample size is statistically valid, the 79% finding can be projected to the entire population from which the sample was selected. Simply put, this is quantitative research. Qualitative research, is much more subjective than quantitative research and uses very different methods of collecting information, mainly individual, in-depth interviews and focus groups. The nature of this type of research is exploratory and open-ended. Small numbers of people are interviewed in-depth and/or a relatively small number of focus groups are conducted. Participants are asked to respond to general questions, and the interviewer or group moderator probes and explores their responses to identify and define peoples' perceptions, opinions and feelings about the topic or idea being discussed and to determine the degree of agreement that exists in the group. The quality of the findings from qualitative research is directly dependent upon the skill, experience and sensitivity of the interviewer or group moderator.

The term "Epidemiology" comes from three separate words: "epi" - which means "upon," "demos" - which means people/population, and "ology" - which means the science. Hence it means the study of things that occur upon the population. Epidemiology is the study of how diseases and other health outcomes are distributed in the population and the factors that influence or determine this distribution.

Today, research is increasingly diverse in its objectives, scope and modes of organization. Research involves individual endeavors, small and large teams, major regional or national research networks, and international consortia. The need to concentrate intellectual and financial resources has spurred the creation of new research centers and institutes that transcend the traditional academic organization based on disciplines. Budgetary pressures and the benefits of collaboration encourage the pooling of expertise…… [read more]


Algebra Lesson Plans and Curriculum Term Paper

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(p. 38).

A large category of algebra misconceptions has been documented in Algebra: Some Common Misconceptions under the category of "The Meaning of Letters." These relate to students' difficulty with the meaning of letter variables. They may completely ignore letters and consider them irrelevant. For example, add 3 to x + 4 and the answer is 7. Or they may… [read more]


Multiplicative Number Theory Term Paper

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All integers are divisors of 0. All integers 'a' are divisible by and If a has any other divisors, then it is called a composite. Otherwise, it is called a prime, unless which are called units. Of the positive integers not greater than 20, the composite numbers are

The prime numbers less than 20 are

Primality testing and factorization

The… [read more]


Frege's Much-Discussed Book, the Foundations Book Review

Book Review  |  4 pages (1,207 words)
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"

Importantly, Frege argued that analytic judgments govern the laws of arithmetic, and thus these laws exist a priori. This analysis was likely one of the most important contributions of The Foundations of Arithmetic.

As defined in The Foundations of Arithmetic, Frege's main analysis that the laws of arithmetic are a priori has important consequences. Frege notes that the definition of the laws of arithmetic as a priori results in the following: "Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction."

Frege has a great number of influential and important admires. For example, the well-known philosopher Michael Dummet notes that Frege's work on the criterion of identity is "brilliant and philosophically fruitful." Further, Dummet gives Frege high praise for uniqueness, noting that The Foundations of Arithmetic is truly the first work of analytical philosophy (Frege Biography).

In spite of the great praise heaped upon the book, Frege's analysis is sometimes somewhat flawed. For example, Frege's analysis is often somewhat weak in terms of psychological references. He easily notes the difference between concept and object, and yet he does not clearly define sense and references. Barbosa notes that after The Foundations of Mathematics was written, Frege rejected his contextual preference, which argued that words refer to something based on context.

Frege has also been accused of distorting the ideas of other philosophers to his own benefit. Notes Barbosa, "Sometimes (Frege) distorts a little bit what others say about logic, so he argues against those thinkers more effectively." This is indeed a serious criticism, and implies that Frege was, at least in this case, not scrupulously rigorous or honest in his philosophical arguments.

Frege was always willing to correct inconsistencies in his works, and the issue of contextual preference was no exception. Barbosa notes that after Frege "wrote the book, he would reject this principle, because of his doctrine of sense and reference: the sense of the words determine the sense of the sentence; and the reference of the words determine the reference of the sentence."

In conclusion, Gottlob Frege's The Foundations of Arithmetic has made a lasting and influential contribution to the philosophy of mathematics. This book is essential reading for anyone interested in the philosophy of mathematics, and is also invaluable for anyone interested in the broader field of analytical psychology. The Foundations of Arithmetic provides a convincing argument that logic is the basis of arithmetic, rather than psychology, and also makes the important argument that analytic judgments govern the laws of arithmetic, and thus these laws exist a priori. It was in these discussions that Frege likely made his greatest contributions to the philosophy of mathematics. Despite his great critical success and long-lasting influence, Frege's works were not without their weaknesses. Importantly, many psychological terms within The Foundations of Arithmetic are not thoroughly defined, and critics have argued… [read more]


Power of Statistical Analysis Term Paper

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The mean, median and mode are all equal in this type of measurement, and the scores at either end of the distribution, those which are extremely high, or extremely low, occur less often. For example, a curve representing the results of an intelligence test would have the highest number of people in the middle, or measuring within the 'average' intelligence… [read more]


Nursing Research Report the Structure Term Paper

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Other considerations that a researcher must account for within the design section of the study are directly related to the manner by which a sample has been selected, the fashion by which the assessment instrument is administered, possible limitations and delimitations surrounding the investigation, and the applied control procedures. Should these factors not be taken into account there exists a… [read more]


Scientific Investigation Includes Both Independent Term Paper

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This particular type of ANOVA shows differences that are a result of "effect" and not differences between mean scores. Again, a wrong choice was made.

Assuming the "t" test were the appropriate tool the authors failed again in not pre-selecting their level of statistical acceptance. Whether or not this was a clever move on the part of the authors or not is not know. What is being implied here is that when there is no stated testable null hypothesis there is no reason to pre-set an alpha or probability level for accepting or rejecting the null hypothesis. In cases like this researchers are free to explain any result they choose to and not bound by controls pre-set in the beginning of the study. This, as most research pundits would express is sloppy research.

Results and Implications Because of all the errors in research design, measurement instrument selection, and statistical tool selection interpreting the results of this study cannot take place. The errors are so great that offering an interpretation of the results would only add error to error. At not time can there be faith placed in research findings that are fraught with error. To warrant the results of this study as being useful to the advancement and understanding or learning disabled student simply cannot take place. The bar of excellence must be raised significantly for this study to garner support, as the external error for this study is magnanimous. What is suggested is as follows:

Restate the research question in proper investigative form.

Specifically state all testable null hypotheses.

Pre-set a probability level for the acceptance or rejection of any and all null hypotheses

Select statistical tools that can effectively analysis data gathered in support of the specific research question.

Fully expound upon the measurement tools used to collect the test data to be analyzed.

Specifically state the limitations and delimitations of the study

Support the need for such a study through a review of literature

Explicitly define the terms used in the study including both independent and dependent variables.

Explain all testing procedures in detail.

List all possible intervening variables and internal and external error.

Make use of…… [read more]


Permutations and Combinations Term Paper

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(Dr. Math, 2004)

Beyond speculating about advertising, however, the use of permutations and combinations can be useful, for instance, when a business desires to allocate its advertising for several products along several potential sources, all from the same media such as television or magazines, but wishes to make sure that the combinations of the different publications did not overlap in terms of the combinations. To calculate, the various letters could be used to represent the publications, and the products also allocated various letters, to ensure that there was no overlap of particular products and sources.

Restaurant owners could use permutations and combinations to determine various pairings of toppings, to determine if this was economically feasible to achieve -- for instance, what is the maximum amount of combinations a pizza can have, given a fixed array of toppings, and also, what is the maximum amount of toppings that any singular pie can possess? Thus, the owner could calculate the maximum amount of funds the pizza could possibly allocate to the owner of the pizza business.

Permutations in combination could also be used to pair off different members of staff, when needed, on the floor of a store or a restaurant. For instance, it could be assumed that the establishment would likely have a certain number of tables filled on one particular night, and thus would require a certain number of members of the wait staff, busboys, and cooks, per table, to ensure that the table was adequately attended to over the course of the evening. From an inventory perspective as well, certain products must always be paired together in combination in terms of need, such as coffee cups and stirrers. Thus, permutations in combinations are not simply interesting and speculative statistical tools, but are used in the daily world of business mathematics.

Works Cited

Dr. Math. "Permutations." (2004) Math FAQ. Retrieved on October 7, 2004 at http://mathforum.org/dr.math/faq/faq.comb.perm.html

Dr. Math. "Fast Food Combinations." (2004) Math FAQ. Retrieved on October 7, 2004 at http://mathforum.org/dr.math/faq/faq.mcdonalds.html… [read more]


Experimental Research Research Proposal

Research Proposal  |  3 pages (987 words)
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Experimental Research

One of the many important decisions a researcher must make during his or her work is which design to use for the research. Two main experimental designs include within-subjects and between-subjects design. Each has its own merits and drawbacks, and researchers tend to choose these according to the purpose and nature of the experiments or surveys to be conducted. For the experiment in question, where three different types of survey invitations are offered online, either the within- or between-subjects design can be used.

According to MacKenzie (2013), most empirical evaluations of input devices or interaction techniques, like the one to be conducted here, will be comparative. In this specific experiment, three types of online survey invitations are explored; the first containing only a link, the second offering to donate $10 to charity as a reward for participation, and finally, a chance to win $1,000 as a potential reward for participation. The comparative aspect lies in why people would be moved to respond to each of the invitations, and which invitation would receive the most participants. While some cases require a between-subjects design and others a within-subjects design, this particular survey could be studied by using either.

A within-subject design means that there is one group in which each participant is tested for all the conditions. Two major advantages of this design is that fewer participants are required, which means that recruiting, scheduling, briefing, demonstrating, and all the other aspects of the research procedure would be somewhat easier and take less time. Second, there is less variance resulting from participant disposition. Certain dispositions will occur consistently for certain participants, which makes it easier to make concessions for the particular behavior, as far as it influences the experiment results. Further, differences among measurements will then be due to differences in the conditions being measured rather than to disposition or behavior differences among participants (MacKenzie, 2013).

In the Zikmund experiment, a within-subject design would mean a single group of people would be tested for each type of survey invitation. In practical terms, this would mean that the group would be exposed to all three invitations and asked to choose the one they would most likely participate in. They could also be asked to give reasons for their participation. This would include both quantitative and qualitative effects in the experiment results. Quantitatively, the results would then reveal the invitation that is most enticing to participants, while the reasons can be investigated for their consistency with the results and among each other.

Although within-subject designs have distinct advantages, it is also true that there could be interference between the conditions imposed. When exposed to all three choices, for example, some participants may experience some difficulty choosing among them, which could compromise the reliability of the results. For this reason, researchers sometimes choose to opt for a between-subjects design instead (MacKenzie, 2013).

According to Shuttleworth (2013), a between-subjects design refers to an experiment that involves more than…… [read more]


Meyer Et Al. Meyer, Wang Essay

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In the data. Different methodologies designate the types of conclusions that can be made from the analyses. For example in the current study Meyer et al. (2009) employ a correlational design, therefore they are unable to make causal inferences but can describe the relationships, their relative strengths, and in some cases direction given the analyses.

The type of data also influences the type of analyses one can do. There are a number of different levels of measurement in the current study due to a large number of variables ranging from nominal (e.g., diagnoses or patient employment status), ordinal (e.g., employment status coded as full-time, part-time, or casual), to ratio level variables (e.g., years of nursing work experience). Some of the variables are categorical such as employment status and some variables are continuous variables such as age.

Meyer et al. (2009) used multiple data collection methods that included collecting hospital records, daily unit data, surveys, and patient data forms. In order to ensure that different data sources and collection methods were consistent they calculated the inter-rater reliability for all measures (which they claim was at 90% throughout the study). The use of surveys in the study was extremely important as surveys allow the collection of anonymous data (no identification on the part of the person that takes a survey so they are free to answer candidly) and questions can be asked and rated on scales that allow the researchers to calculate such important internal constructs as a nurse or patient's attitude, opinions, and also allow to collect hard external data such as the number of hours worked, education levels, etc. Surveys remain an important staple in all areas of correlational research as the data can be coded and easily subject to statistical analyses; however, survey data typically does not allow the researcher to determine cause-and-effect associations (Tabachnick & Fidell, 2012). Thus, survey data can be extremely useful, but has limitations.

References

Jackson, S.L. (2012). Research methods and statistics: A critical thinking approach (4th

ed).Belmont, CA: Wadsworth.

Meyer, R.M., Wang, S., Li, X., Thomson, D., & O'Brien-Pallas, L. (2009). Evaluation of a patient care delivery model: Patient outcomes in acute cardiac care. Journal of Nursing Scholarship, 41(4), 399-410.

Tabachnick, B.G., & Fidell, L.S. (2012). Using multivariate statistics (6th…… [read more]


Multivariate Analysis Is Appropriate Essay

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discrete data), or make an unlimited number of comparisons. Like any research tool multivariate statistics have their limitations. Different types of multivariate tests allow a researcher to answer different types of questions, but a researcher's ability to make inferences is always limited by the type of data collected in the methodology used to collect it.

I am interested in how gender rates differ in cases of human trafficking into the United States. Currently there is a study that proposes looking at the differences in gender in human trafficking cases based on the data from The National Human Trafficking Resource Center. This particular to the research could be adequately performed using a simple t-test or one-way ANOVA. However, other variables could be added to the methodology and multivariate analyses could offer much more information regarding the differences in males and females involved in human trafficking. Using other variables such as geographical area trafficked to (e.g., in the United States this could be divided into Midwest, North, South, etc.), the type of context into which human victims are placed (e.g., hard labor, domestic work, prostitution, etc.), ethnic background of the trafficked individual, and others allows for a richer analysis. In this case there would be multiple independent variables that can contribute to the differences in the number of males and females that are trafficked into the United States and multivariate techniques such as factorial ANOVA (or its counterpart multiple regression depending on the type of question) is more appropriate. In this type of study we would expect that the particular context would lead to differences in the rates of males and females trafficked into the country. For example, we would expect that people put into hard labor jobs such as… [read more]


ANOVA: Fobt, Tukey's HSD, and Effect Size Calculations Essay

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Statistics and Probability

A researcher investigated the number of viral infections people contract as a function of the amount of stress they experienced during a 6-month period. The obtained data:

Amount of Stress

Negligible Stress

Minimal Stress

Moderate Stress

Severe Stress

What are Ho and Ha?

Ho: Stress levels experienced during a six-month period does not have a significant impact… [read more]


And Standard Deviation Case Study

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87, which is outside of the confidence interval.

The null hypothesis is therefore rejected -- the bottles contain a mean fill that is lower than the fill allowable within the 95% confidence interval. The complaint is correct -- the bottles are not sufficiently filled.

There are a couple of reasons why the bottles are not being filled properly. Most likely this is a calibration issue with the filling machine. The machine is chronically underfilling, which is most likely explained by calibration. The actual volatility of the fills (standard deviation) is high but does not explain the strong deviation from the expected mean of 16.0.

To solve this problem, I would check the calibration of the filler. Normally, the filler will fill to a level around the mean, usually at the 95% confidence interval -- or better if it is a more expensive filler. So if the machine is doing that here, it clearly thinks that 14.9 ounces is 16 ounces, or somebody changed the target fill level to 14.9 from 16. So the machine either needs to have its fill level target…… [read more]


Limit Your Summary Term Paper

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Low working memory individuals did not suffer appreciably under pressure, showing that working memory is indeed crucial to success and also sensitive to pressure constraints such as social evaluation.

8. How are these findings relevant to everyday life? Provide at least two examples. At least one of these examples should be an original example. That is, it should not be mentioned by the author(s) of the research article.

These findings are highly relevant for a number of real life scenarios. One example is in school children or in students at university level. Students who do well on their homework and low-pressure class exercises might choke under pressure, such as when they are a leader of a team, when there are time constraints on them, or when they are being watched closely. Another example is in the workplace. Employees who depend on their working memory might choke in high-pressure scenarios, such as public speaking engagements or competing with a colleague for an important contract. The implications are that persons who have a high capacity for success should develop their skills in coping with anxiety.

9. Describe two ways in which this research expands upon the theories and concepts discussed in class? You may wish to consult your textbook and lecture notes. Please cite appropriately (in APA format) when you discuss information from your text (e.g., Goldstein, 2011) and from your class notes (e.g., Trammell, personal communication, 2013). Please limit your response to 8 sentences.

The theories and concepts discussed in class have to do more with general cognitive psychology. Short-term memory is discussed, but not in terms of working memory in the context of performance on cognitively demanding tasks like mathematics. We have not learned that working memory is like a flash drive, in that the brain is able to process material effectively and rapidly by relying on short-term memory space. Yet anxiety also takes up this short-term memory space. Invading working memory, anxiety therefore inhibits performance. This would seem to be true for everyone, but it is especially true for those who rely most on short-term or working memory. It appears that the most successful or most capable persons are those who rely strongly on their working memory.

10. What research questions remain unanswered? That is, describe at least two areas for future research. Please limit your response to 8 sentences.

This study raises several questions for future research. One is related to the different effects of different types of pressure. It would be helpful to know what types of pressure affect what types of people. For instance, some people might not find financial incentives stressful and would therefore not have any problem being distracted by that stimulus when solving math problems. Other people might find that social pressures are less important. It would also be helpful to know if time constraints and other factors are relevant. Furthermore, it would be interesting to know if there are gender differences between high capacity persons. Another question for future research is how… [read more]


Solved Problems Term Paper

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Statistical Estimates

(the Number That Appeared The Most In The Data)

median: (7. 30 + 7.60) / 2 =

mean:

range: 8.90-6.60 = 2.30 (Highest number = 8.90, lowest number = 6.60)

Computing standard deviation sample standard deviation =

sample mean =

sample standard deviation =

Using the empirical rule

68% of values lie within mean ± standard deviation

95% of lie within mean ± 2 standard deviation

% lie within mean ± 3 standard deviation

Given mean = 120cm, standard deviation = 12cm

Let x represent percentage of values,

Then, mean ± standard deviation = 120 mm Hg ±12 mm Hg

=108 mm Hg

132 mm Hg

mean ± 2 standard deviation = 120 mm Hg ±24 mm Hg

= 96 mm Hg

144 mm Hg

Thus, the approximate percentage of women between 96 mm Hg and 144mm Hg is 95%

Implementing Chebychev's theorem

Z-score (critical value)

Given that -2.37 is less than -2.00 or 2.37 is greater than 2.00, we may consider this value as unusual

Chapter 4

1. Probability estimate

2. Probability odds

3. Probability odds

The outcomes could be 1 or 2 or 3 or 4, and these are mutually exclusive events. Thus,

P (rolling a number less than 5) = P (1 or 2 or 3 or 4)

= P (1) + P (2) + P (3) + P (4)

= (1/6) + (1/6) + (1/6) + (1/6)

= 4/6 = 2/3 [Answer…… [read more]


Easy Explanation of Analysis of Variance Essay

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¶ … goals of statistics is to create an easy way to compare two or more factors in a meaningful way. Basic comparison tests, such as the t-test, allow for the comparison of two groups. Analysis of Variance (ANOVA) allows for the comparison of three or more different groups. While the concept of ANOVA may seem complex, it is simply a way of describing how the various items that belong within a single large group vary from one another. This can be very important because there are two main types of variance in a group. One type of variance is the type of variance that can be found naturally within a group; this type of variance is frequently referred to as random variance and may also be described as in-group variance. The other type of variance is the type of variance that is caused by the impact of independent variables on the dependent variable and may also be described as between-group variance. Without understanding the underlying variance in a group, one could overestimate or underestimate the impact that an independent variable was having on the dependent variable. An ANOVA test does not provide conclusive data; instead, it provides analysts with a key to understanding other test results, so that they can understand the significance of those results (Investopedia, 2015).

An ANOVA test can help explain whether there are any significant differences between the average results for three or more different groups. In an experimental context, each of the three groups will be as similar as possible at the beginning and the in-group variance can help explain how much variation is simply the result of random chance. Then, once the independent variable is applied to the group, the changes are examined to determine what type of impact the independent variable has on the dependent variables. The goal of the ANOVA is to test the null hypothesis, which is a hypothesis developed for the purpose of research, which states that the independent variable will have no impact on the dependent variable.…… [read more]


Hypothesis Testing Essay

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Alpha level determines the confidence with which the researcher can decide to reject the null hypothesis. When researchers establish an alpha level prior to performing the research they are essentially deciding that if the null hypothesis is true then the probability of getting significant results in this study by either sampling error or by chance is whatever the alpha level they have set is (conventionally set at 0.05; Runyon, Coleman, & Pittenger, 2000). The choice of the alpha level is arbitrary, in other words researchers decide where to set it before their analysis. It is been a convention in research to use the 0.05 level; however, this is certainly not set in stone and recently this convention has come under some sharp criticisms (e.g., see Ioannidis, 2005). There are times when researchers will decide to use a more liberal or conservative alpha level in the research.

For example, suppose that a researcher is developing a way to diagnose a very serious and debilitating disease that typically cannot be diagnosed until the infected individual is nearly terminal. Also let us assume that if people with this disorder can be identified before it becomes terminal the cure is relatively safe. In this case the cost of making false positive errors (Type I errors) is low whereas the cost of making a false negative error (Type II error) is considered high and researchers are often motivated to increase their decision -- making criteria by raising their alpha level (Runyon et al., 2000). Also when researchers are investigating areas where there is very little known about the potential outcome and they are trying to develop theoretical models they may also decide to use a more liberal alpha level in order to identify potential significant constructs that will be scrutinized more conservatively in the future.

There also times when researchers will opt for a more conservative alpha level. In fact, there is one specific situation where researchers should adopt a more conservative alpha level but often do not. This occurs when researchers are making multiple statistical comparisons on the same data set (e.g., when the comparisons are not independent of one another; Runyon et al., 2000). The Type I error rate for any single statistical comparison is set by the researcher prior to their analysis and this is the…… [read more]


Exploring the Correlation Between Age and Cell Phone Use Chapter Writing

Chapter Writing  |  3 pages (732 words)
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Computer Lab: Hypothesis Testing Correlations

The following null hypothesis is applicable for testing the correlation between the two variables "Age" and "Q18: "On an average day, about how many phone calls do you make and receive on your cell phone?"

Ho = The age of the cell phone user is not related to the average number of cell phone calls made or received by the cell phone user.

The Pearson correlation coefficient is .055 (p = 0.05, 2-tailed). In addition, Spearman's rho (-.244) and Kendall's tau (-.340) both show the correlation as significant at the 0.01 level (2-tailed). The null hypothesis is rejected at 0.01. There is a positive relationship between the age of the cell phone user and the average number of cell phone calls made or received by the cell phone user.

The number of observations for the "Age" variable was 1917 and the number of observations for the "Q18: "On an average day, about how many phone calls do you make and receive on your cell phone?" variable was 2252. User-defined missing values were treated as missing. Statistics for each pair of variables was based on all the cases that had valid data for that pair.

The assumptions about the data, including normality and linearity, were tested by examining the descriptive statistics and tests for skewness and kurtosis as shown in the output table directly below. The data are assumed to be normally distributed and independent. Some outliers are present in the data, which is to be expected since not all frequent users of cell phones are young. Variables such as the type of work or employment in which cell phone users engage can strongly influence the frequency of the cell phone calls made and received. These considerations encourage additional statistical analysis of other variables and perhaps additional research.

Statistics

Q18. On an average day, about how many phone calls do you make and receive on your cell phone?

AGE. What is your age?

N

Valid

1917

Missing

0

Mean

46.99

52.06

Std. Error of Mean

4.295

.412

Median

5.00

52.00

Mode

10

60

Std. Deviation

19.565

Skewness

4.807

.170

Std. Error of Skewness

.056

.052

Kurtosis

21.367

-.544

Std. Error of Kurtosis…… [read more]


Math Problems and Concepts in Teaching Research Paper

Research Paper  |  2 pages (725 words)
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Mathematics of Mathematic Puzzles

Using mathematics puzzles is a frequently-used deployed pedagogical device to teach critical concepts to math students of all ages. "Understanding in mathematics is born not only from formulas, definitions and theorems but, and even more so, from those networks of related problems… Mathematicians seek knowledge. In search of knowledge, they enjoy themselves tremendously inventing and solving new problems" (Bogomolny 2015). The mathematics of puzzles is also designed to challenge the student's instinctive conceptions of how the world works. For example consider the question posed 1702 of how long would a rope encircling the earth have to be "for it to be one foot off the ground all the way around the equator -- this can be used to illustrate the geometric concept of finding the circumference (Pickover 2010). The student's intuitive instinct would be that the rope must be extremely long but in fact the answer is only 2pi. "If r is the radius of the Earth, and 1 + r is the radius in feet of the enlarged circle, we can compare the rope circumference before (2pir) and after (2pi (1 + r))" (Pickover 2010).

Other examples of these teaching devices are the multiplying 'wheat on a chessboard' dilemma. In this problem, the grains of wheat, beginning with one, are doubled every square leading to such a proliferation of grains that it would be impossible to provide that much wheat in reality, thus illustrating the concept of geometric growth (Pickover 2010). There is also the barber's paradox "which involves a town with one male barber who, every day, shaves every man who doesn't shave himself, and no one else" which is used to illustrate the concept of set theory (Pickover 2010).

The applicability of apparently pointless mathematical queries to vital foundational concepts in math has also come to light in the evolving discipline of game theory, frequently used by economists to illustrate how people make choices. For example, in the classical case of the Prisoner's Dilemma, two separately-imprisoned individuals are placed in a cell. If neither confess, both men go free, if both confess, both get a reduced sentence but still do jail time, while if only…… [read more]


History and Math Puzzles Research Paper

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Mathematical puzzles are not simply fun and interesting topics on which to muse: they have great significance within the history of the discipline, often connecting many generations of mathematicians who strive to unravel such riddles. "What is the value of such puzzles and enigmas? One important value is the fact that a math puzzle has an answer. We spend much of our time puzzling over problems that do not appear to have easy answers, if they have answers at all, and math puzzles offer a simplified way of solving problems that lead to a satisfying conclusion" (Bright 2010). Math problems are frequently-deployed mental exercises to help individuals understand certain concepts better. But some math problems have been so widely regarded as unsolvable they have become notorious.

Amazingly, many of the earliest puzzles were only solved in the modern era. For example, the Greek Archimedes constructed a puzzle asking how many ways there were to divide a square into 14 pieces. Only in the 21st century did a Cornell professor of mathematics discover that there "are a total of 17,152 solutions, but some can be considered equivalent if a rotation or a reflection are performed" (Pitici 2008). In another famous mathematical puzzle pertaining to spatial relations called the bridges of Konigsberg, the central problem arose when "seven bridges were built so that the people of the city could get from one part to another;" people began to speculate how to walk over the various bridges to go straight across the city while crossing each bridge only once ("The beginnings of topology," Math Forum). The problem of the bridges was one of the first questions ever posed in the evolving discipline of topology in mathematics, which reflects the fact that the "properties of the shapes remain the same" regardless of whether they are "stretched or compressed" ("The beginnings of topology," 2015).

The concept of paradoxes was also highly significant to the discipline of mathematics. Zeno's paradox about the "infinite divisibility" of space asked the question of how motion was possible ("Zeno's paradox," 1998). Obviously, motion is possible from an observable perspective but in theory motion is impossible because to reach one point, first we need…… [read more]


Dislocation Dynamics in an Anisotropic Stripe Pattern Research Paper

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Crystal Review

A review of "Dislocation Dynamics in an Anisotropic Stripe Pattern"

This paper reviews the findings of a specific published study regarding the patterns that emerge form dislocation occurring across domain walls in physical systems, and specifically anisotropic stripe patterns. Different electromagnetic and conductive patterns emerge due to the striped patterns that are created by distortion movement occurring parallel to domain walls, and the study reviewed examines the nature of these variances and the degrees of distortion and pace of change that occur. Analysis of the article published as a result of the study is also conducted form a quantitative and qualitative/critical perspective, for which other related studies and information are utilized.

Topological defects occur in almost all crystals, though they vary in their mathematical complexity and the solutions/theories that have been used to examine and explain the various defects. Boundary conditions, which in crystals take the form of domain walls, cause these topological defects, defined as the dislocation of the crystal. These distortions their causes and their effects have all become major areas of study; the study of topological defects has increased as it becomes clear that they are the dominant pattern in many kinds of physical systems, including in crystals. Uniform systems have yielded simpler understandings in regards to their topological defects than non-uniform systems, providing the impetus for the study reviewed and for this critical analysis of this study.

The article does an admirable job of providing an overview of the research regarding domain growth and topological defects generally, though the language is highly technical -- unnecessarily so, at points. The temporal evolution of these patterns and domain shifts in uniform and homogenous systems of several different types, including fluid systems and magnetic systems, are provided in the introductory material to provide an avenue for comparison and analysis in the striped systems analyzed by the researchers. Electroconvection is identified as an anisotropic system, with its own specific patterns of development: normal and oblique rolls. Specification and understanding of the impact of non-isotropism in systems on the electroconvection, however, remains largely underdeveloped, and the authors make a good case for the necessity of their study and both the understanding and the attention it provides to this unique yet fairly common occurrence.

The anisotropy of domain wall growth is identified as the…… [read more]


Regression Analysis Is the Technique Term Paper

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Regression analysis is the technique used to express the linear relationship between two variables. With this technique we can estimate the value of the dependent variable (Y) based on a selected value of the independent variable (X). This kind of analysis is mostly used to determine if sales numbers of a product a are related to the number of TV advertisements for that particular product during a specific timeframe. The mathematical equation for the line used to estimate the value of variable Y on the basis of variable X is also known as the regression equation (general form of linear regression equation: Y1 = a + bX) (Lind, Marchal, & Wathen, 2005).

Y1

= read Y prime, is the predicted value of Y for a selected X value a = is the Y-intercept, or the estimated value of Y when X = 0

b

= is the slope of the line, or the average change in Y1

X

= any value of the independent variable that is selected

Linear regression is used to make predictions about a single variables value. In other words, it is used for discovering the equation for a line that most closely fits the given data (Lind, Marchal, & Wathen, 2005). That linear equation is then used to predict values for the data. For example: A sales manager wants to know if more sales calls will sell more copy machines, and by how much the number of calls have to increase to reach a certain number of sales for those machines. The main components are the slope and the intercept, also the standard errors and confidence intervals. Furthermore the correlation coefficient, and standard deviation are components of the linear regression analysis.

Simple regression - the simple…… [read more]


Alcohol Abuse Among the Elderly Essay

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SAMPLE TEXT:

¶ … Sampling error" is the term applied to the discrepancy and possibility of being misled by observing only a sample of a total population instead of the whole population itself. Generally speaking, the larger and more diverse the sample population is, the lower the risk of sampling error, because the sample will be more representative

A sampling distribution of means is a distribution of means collected from different sample populations. That is, it is a distribution created by calculating the mean of specific responses given by subjects within several distinct sample populations. For instance, if the mean from sample a is two, from sample B. is three, from sample C. is two and so on, the sample distribution of means would show the data spread of these means (around two or three, in this example).

3)

The central limit theorem basically states that no matter what the distribution of original data is, the sampling distribution of the mean will approach a normal distribution, and the larger the sample is (for many distributions and for the sampling distribution of the mean) the closer it will approximate a normal distribution.

4)

The confidence level of a data set or figure is the degree of certainty that one can have in that figure or data set, whereas the confidence interval is the actual range of data that is contained in the confidence level percentage of the data set.

5)

Statistical significance refers to whether or not an observed trend, correlation, or other relationship actually appears to exist after rigorous examination of the numbers, and not merely due to…… [read more]


Search for Knowledge or Data Essay

Essay  |  3 pages (1,154 words)
Bibliography Sources: 3

SAMPLE TEXT:

¶ … search for knowledge or data about a matter, investigating the subject via scientific methodology. The primary process of research is to discover, interpret, and (in the case of applied research) use certain methods that will lead to more reliable, evidence-based knowledge about our world.

The research process is based on the following steps: 1. Articulation of the topic and literature review or observations; 2. Researcher's hypothesis; 3. Conceptual definitions and operational definitions of investigated concept; 4. The scientific gathering of data; 5. The scientific analysis of data; 6. Modifying or support of hypothesis, and 7. Conclusion (Trochim, 2006).

Qualitative research is often best used when the sample under study cannot be analyzed in the laboratory and one wants richer information on that population sample. It is usually applied to people. Five examples are: (i) Margaret Mead's case study and observations of Samoa; (ii) the in-depth analysis and observations of a program in order to assess its operational success (e.g.. Of UNICEF); (iii) assessing individual people (e.g. children (as was done with Piaget's clinical method) to assess the way they work; (iv) naturalistic observation- studying a culture in an unobserved natural manner; or (v) investigating biographical details of an individual's life.

3. On one level, this may be called 'interviewing' either individually or through focus groups where the researcher (using open-ended or closed-ended questions or a mixture of both) elicits the opinions and particular perspective / experience, and so forth, from an individual on a certain matter.

On a deeper level, this may be described as phenomenological research (conducted through protocol methodology) where the participant is asked to record naive descriptions of his experience and the researcher closely assesses these (Breakwell, Hammond, & Fife-Schaw, 2000).

4. The arguments for quantitative research revolve around the fact that bias is more closely screened out when the study is conducted in a rigid laboratory-type methodology with statistical data and measurements used to quantify their significance.

The qualitative approach, however, maintains that many cases, especially those involving humans, cannot always be assessed in such a manner. Certain data (such as emotions of hostility, love etc.) are too abstract to be measured, and humans and events involving humans are too chaotic to be 'pinned down' and quantified in a laboratory environment.

6. The checklist here would involve operational definitions of the following variables: Concepts involved in 'caring': the range of activities that involve looking after the cat and the intensity to which individual does so. Life expansion would be defined -- i.e., the exact amount of years that would be used as measurement to indicate that caring for cat does prolong life; hypothesis would also consider the phraseology 'living alone' -- does he/she have close friends / immediate / extended family who care for individual; is he/she involved in community events and, if so, to which extent; does he/she receive social support in any particular manner and the extent of this social / family support would be considered. Furthermore, 'Northwestern region' would be defined.… [read more]


Chi-Square With Base Hypothesis That All Political A-Level Coursework

A-Level Coursework  |  3 pages (731 words)
Bibliography Sources: 6

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¶ … Chi-Square with base hypothesis that all political groups contribute equal amounts.

b) Chi-square with base hypothesis appropriate to the attitude question asked.

c) T-test.

d) Chi-square with base hypothesis of equal average salaries between regions.

Perform a chi-square test of the following data:

a) Regulation is the best way to ensure a safe workplace

Managers

Blue-collar workers

Agree

Disagree

Totals

One potential hypothesis for this data is that managers and blue-collar workers do not have very different opinions about regulation. Some regulations may make the workplace safer for managers as well as blue-collar workers. Many blue-collar workers are politically conservative, which would influence them against over-regulation of the workplace. So, the expectations for my chi-square test will be:

Managers

Blue-collar Workers

Agree

Disagree

No Opinion

Total

Expected

Obtained

(Obs-Exp)^2/Exp

Man-agree

62

58

0.258064516

Man-disag

29

34

0.862068966

Man-NA

9

8

0.

Work-agree

62

66

0.258064516

Work-disag

29

24

0.862068966

Work-NA

9

10

0.

2 = 2.46

This does not exceed the critical value of 3.84 for a chi square test with ? = 0.05 and df = 1. Therefore, we can assume that these data are not significantly different from the expected values, and do not violate the null hypothesis.

b) Ownership of residence

Male

Female

Yes

25

16

No

7

8

Totals

32

24

In this case, we are testing current numbers against the null hypothesis that home ownership has equalized across genders. The expected value table is:

Male

Female

Yes

23.4

17.6

No

8.6

6.4

Totals

32

24

Expected

Obtained

(Obs-Exp)^2/Exp

M-Yes

23.4

25

0.105400697

M-No

8.6

7

0.288095238

F-Yes

17.6

16

0.140534262

F-No

6.4

8

0.384126984

In this case as well, we fail to violate the null hypothesis, ?2 = 0.92.

c) Age of shopper

Store a

Store B

20-34

27

73

35-54

31

82

55+

11

93

Totals

69

The null hypothesis in this case is that both stores draw equally from the same age groups, although Store B. draws more customers overall. The expected value table is:

Store a

Store B

20-34

21.8

78.2

35-54

24.6

88.4

55+

22.6

81.4

Totals

69

Expected

Obtained

(Obs-Exp)^2/Exp

20-34

21.8

27

1.25830064

35-54

24.6

31

1.66726748

55+

22.6

11

5.98240235

20-34…… [read more]


Journal of Physics and Medicine in Biology Book Review

Book Review  |  7 pages (1,875 words)
Bibliography Sources: 1

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¶ … Journal of Physics and Medicine in Biology: Manuscript 653

"A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density" by Webb and Nahum (1993)

The following paper critically evaluates the basis of the article entitled Re: "A model for calculating tumour control probability in radiotherapy including the… [read more]


Function Establishes the Relationship That Exists Case Study

Case Study  |  2 pages (434 words)
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Function establishes the relationship that exists between different variables, more precisely, between the input and output variables. The input variables will be linked to the output result through a general formula or function: through the input of the variables into the formula, the final output will result. One important condition for a relation to be considered a function is for each x value to result one and solely one f (x) value.

A linear function is a function which has only one variable and it is, at the same time, a first degree function. The general formula of a linear function is f (x) = ax + b, where a and b are real constants and x is the input variable.

As previously mentioned, the standard form of a linear function is f (x) = ax + b.

The slope of a line is a in the function f (x) = ax + b. As such, the formula to calculate a is a = (f (x) -- b)/a

Let C. be the number of cups that are sold and P. The price for which the cups are sold. The total money that can be raised through the lemonade stand is given by the function f (P) = C * P, following the notation previously mentioned. In that…… [read more]


Spiritual Principle: For Unto Term Paper

Term Paper  |  2 pages (446 words)
Bibliography Sources: 4

SAMPLE TEXT:

Spiritual Principle:

For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. (KJV Matthew 25:29)

Students will learn to investigate and solve piecewise functions; they will learn to explore exponential functions by extending properties of exponents to include all integers; they will learn to solve quadratic equations in one variable by using factoring, square roots, and the application of the quadratic formula; and, they will be able to discuss functions and their inverses by using concepts such as one to oneness, domains and range.

Suggested Activities and Experiences:

Divide students into groups of approximately six each. Students will make a table and graph in pencil. Three students in the group will graph the linear function and three will graph the quadratic equation. The group of six will come together and put their graphs together and describe and evaluate the piecewise functions.

2. Students will memorize exponent integers and be able to explain their characteristics. Once these concepts are understood, students will move on to solving simple exponential equations and inequalities as well as graphing functions. To assist the students, games such as MathDork (http://www.mathdork.com/games/asteroidsexp3/asteroidsexp3.html) can be played at home or during computer lab time at the school.

3. To solve quadratic equations, students will…… [read more]


Qualitative vs. Quantitative Research Essay

Essay  |  2 pages (622 words)
Bibliography Sources: 1

SAMPLE TEXT:

Qualitative vs. Quantitative Research

This article analyzes the distinctions between Qualitative and Quantitative Research Methodologies and discusses seven distinct research criteria and how each method differs regarding them. This first Criterion, Epistemological Assumptions, also generally describes the features of both methods. Quantitative research seeks to discover and objective and quantifiable reality independent of feelings or thoughts about it. While qualitative research ascribes beliefs, feeling and thoughts regarding reality and describes it in a varying non-absolute scale. Often the researchers own beliefs about what they are trying to accomplish can influence their selection of research methods. But the parameter for choosing one or the other generally guided by criterion two, Purpose. If the purpose of the study is to garner information about a predictive future state, than quantitative research is generally chosen. More aligned with number theory, quantitative analysis can yield more predictable and graphic results for decision making based on current states. In other words, "generalizability" is the key. Whereas, if a study's purpose is to understand and interpret research that requires a more in-depth methodology that will dig deeper into motivations and beliefs, qualitative methods are usually employed. Here also sample size has less relevance that in quantitative research.

Raw Data, criterion three, is presented quite differently in these methods. Quantitative data, as the word implies, regards quantity or numerical differentiation as key. It is not so much what is said, but how many times an instance occurs or what value can be placed upon it. Whereas qualitative data is usually composed of words whose meanings regarding information can include various media and formats as well.

The next criterion, emphasis, is similar to purpose, as it is the overall intention of the study and the researcher point-of-view. In quantitative research the emphasis is on repeatability and predictability. The results show that there is a trend or tendency and that they…… [read more]


Social Research There Are Several Explanations Essay

Essay  |  3 pages (956 words)
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SAMPLE TEXT:

Social Research

There are several explanations for an observed relationship that need to be examined and dismissed before a true relationship can be established. First, it is possible that an observed relationship is merely coincidental; using large sample sizes that seem to show the same relationship can diminish this risk. Also, an external cause influencing both of the observed factors could exist, which is why testing or controlling all other variables is necessary to show the validity of a relationship. Finally, it is possible that a researcher bias exists, and again controlling the research methods and variables can help to limit exposure in this area.

A Type I error occurs when the null hypothesis is falsely rejected. In this type of error, the correlation, relationship, or explanation advanced by the alternative hypothesis is accepted -- meaning the null hypothesis is rejected -- due to false observations and/or analyses. A Type II error occurs when the null hypothesis is not rejected even though evidence that it should be rejected actually exists. For instance, the correlation proposed by an alternative hypothesis might actually exist, but due to an error this correlation is not observed or is not seen as significant by the researcher, resulting in continued acceptance of the null hypothesis.

3)

A null hypothesis would be that there is no correlation between caseload size and child welfare worker stress. A one-directional research hypothesis would be that as the size of a caseload increases, the amount of stress experienced by the child welfare worker with this case load also increases. In the research that would investigate this hypothesis, caseload size would be the independent variable or the cause in the causal relationship hypothesized, while child welfare worker stress would be the dependent variable, or the effect.

4)

Probability sampling is also known as random sampling, and can be used to infer information and observations about the general population from which the sample is drawn. In other words, a large enough random sample population drawn from a general population pool would be expected to match that general population in demographics and proportion, and thus the probability of a specific outcome in the population would be the same or similar to observations in the general population. Nonprobability sampling can be useful, but is not entirely random and so cannot be used to make assumptions about a general population.

5)

Some advantages of questionnaires are the ability they provide for respondents to give detailed answers, and the removal of the researcher from the direct data gathering process (i.e. respondents can fill out questionnaires in their own time) reducing research bias or influence on the results. Disadvantages, however, include the potential for misinterpretation or differing interpretations among respondents, reducing the validity of the questionnaire's measures and conclusions. Reduced control generally can be a problem.

6)

Interviews have a strong advantage in the ability of…… [read more]


Scaling Application of Measurement Term Paper

Term Paper  |  2 pages (710 words)
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SAMPLE TEXT:

Scaling can be considered to be a major aspect of exploratory type research and can answer questions like what dimensions are the basis for a set of ratings for example. However, the best use for scaling is for scoring purposes. In other words, scaling is an excellent medium for collecting responses to a given set of items that it is easy to assign a single number with that number indicating an overall attitude or belief.

Scaling then can be said to be a branch of measurement involving the inherent construction of an item that equates 'qualitative constructs with quantitative metric units.' This tool descended from psychology and education because these areas each needed a means for measuring things prior to scaling that were technically no measurable. So it is therefore not difficult to understand why so many individuals simply do not understand scaling. The basic idea of scaling comes from two time periods, unidimensional for instance comes methods developed throughout the first half of the twentieth century and are now usually named after their inventors while later in the 1950s and 1960s, theorists got more involved and created the more difficult concepts of multidimensional scaling.

So in conclusion, "it is important to realize that although a scale is an instrument that can be used alone, it is often integrated into a larger and more complex instrument, such as a survey. (Trochim 2008, p 131) Scaling is a tool that helps clear abstract ideas into measurable context. This work then aimed to discuss the role of scales in research and research design and to point out that measurements that incorporate scale data are often incorporated into learners' quantitative research projects and dissertations. For that reason, it is critical to clearly identify the purpose of scaling and how it can best be utilized in these types of projects. Scaling as a science of measurement is based on specific rules and often assigns objects with numbers so they can measure abstract objects to one another.

References

Trochim…… [read more]


Hypothesis and Stats Thesis

Thesis  |  1 pages (370 words)
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John and Sons Company: Null Hypothesis and Test of Statistical Significance

The null hypothesis often states the opposite of what an experimenter is attempting to prove (Lane 2009). The experimenter wants or expects to disprove the null, which is expressed as H0. For example, presume that the John and Sons Company wants to open a new factory overseas and take advantage of lower wages abroad, but is concerned about the potential quality implications of this move upon the product, as John and Sons have had quality-control problems in the past with their overseas operations. The H0 would be: 'there is no statistically difference in the number of defects in a batch of the product manufactured in country X versus a batch manufactured in the United States.' (Hence the term null hypothesis -- that there is no difference). The alternative hypothesis, expressed as H1, would be that there was a statistically significant difference in the number of defects found in the batches made in country X versus the United States. "This alternative hypothesis states that the relationship observed between the variables cannot be explained by chance…… [read more]


Vectors and Force Thesis

Thesis  |  2 pages (488 words)
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Algebraic Vectors

a) an (x, y) coordinate system would be appropriate; movement will occur both along the sidewalk (i.e. down the street) and across the sidewalk (between the buildings/yards and the curb), requiring a two-dimensional coordinate system

b) a simple x coordinate system or number line is sufficient; the tightrope walker will only be moving in a single direction (albeit wit positive and negative relative magnitude)

c) as stated, only an (x, y) coordinate system would be needed, but in reality a three-dimensional (x, y, z) coordinate system is required to plot submarine and aircraft movements, as travel can occur along the two dimensions of the cardinal directions (i.e. forward-back or North-South and right-left or East-West), as well as vertically (up and down).

b.

3.

a.

b.

Without resolving vectors into components, no understanding of relative motion can actually be established. Vectors are inconsequential if not stated and understood in relation to a fixed point (usually the starting point of the vector).

35m

15m

=25(

=65(

a b

15/sin90 = a/sin25 15/sin90 = b/sin65

15 x sin25 = a 15 x sin65 = b

6.34=a 13.59 = b d+b = 48.59 a = 6.34

48.592+6.342 = 2401.18

( 2401.18 = 49

c = 49 = magnitude

49/sin90 = 6.34/sinA

49 x sinA = 6.34

sinA = 6.34/49

sinA = .129

A ( 7.43( = direction d

c

A

2.5km

5.2km

A

B

B = 180 -- (35-22)

B = 173(

sinB = .122

b2…… [read more]


Experimental Research Design the Research Process Research Proposal

Research Proposal  |  8 pages (2,184 words)
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SAMPLE TEXT:

Experimental Research Design

The research process is stated to be of the nature that utilizes scientific techniques in the investigation of phenomenon and a research process that is focused on acquisition of new knowledge about the phenomenon. (Experiment Resources, 2009) the Experimental method is stated to require the basis of "observable, empirical and measurable evidence, to be termed scientific" and… [read more]


Algebra Suppose You Have a Lemonade Stand Research Proposal

Research Proposal  |  1 pages (355 words)
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Algebra

Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.

C = -60P + 240

Take a look at the table below and write out an equation for f (x).

f (x) -2-2-6-10

f (x) = 4x +

Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f (x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi-part relations so consider all parts when deteriming if they are funcitons.

a. f (x)…… [read more]


Precalculus II Leaning Tower of Pisa Term Paper

Term Paper  |  2 pages (496 words)
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Precalculus II

Leaning Tower of Pisa

The Leaning Tower of Pisa was originally 184.5 ft high. but, currently, the tower is leaning slightly from its original perpendicular state. At a distance of 123 feet from the base of the tower, the angle of elevation to the top of the tower is found to be 60°. Find the approximate angle that the tower is leaning from its original perpendicular state. Then, find the towers current height.

The current height of the tower is BD in the scratch. We can find BD from triangle ABD:

BD=AB*sin

We can find AB using cosine theorem:

BC^2= AC^2+AB^2- 2*AB*AC*cos

BC=184.5

AC=123 cos

25=15129+ AB^2 -2*AB*123*0.5

AB^2-123*AB-18911.25=0 solving this equation we should find only positive root:

D=123^2+4*18911.25

D=90774

D=301.287

AB=(123+301.287)/2

AB=212 sin

A=0.866

BD= 212*0.866

BD=183.59

Answer: tower's height is 183.59 ft.

Part II: Lost Treasure

While scuba diving in Bermuda, you discover a treasure map in a pirate schooner. The map directed them to an area that was no longer there. So, they had to re-create the map by treasure map experts.

The directions on the map read as follows:

From the tallest palm tree, sight the highest hill. Drop your eyes vertically until you sight the base of the hill.

Turn 40° clockwise from that line and walk 70 paces to the big red rock.

From the red rock, walk 50 paces back to the sight line between the palm tree and the hill. Dig there for the treasure.

Mission: Draw the…… [read more]


Pre Calculus II Project Setup: The X-Axis Term Paper

Term Paper  |  2 pages (452 words)
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SAMPLE TEXT:

Pre Calculus II Project

Setup: the x-axis as the water level. The origin is the midpoint between the two x-intercepts/support bases. The clearance level is a horizontal line at QUOTE. Three points are given that are the same for both parabola and semiellipse: the first is the y-intercept, which occurs at 350' above the water, or QUOTE; the two other points are the x-intercepts. The distance between the two supports is 1050', and since the y-intercept bisects both shapes, the x-intercepts are at QUOTE and QUOTE. Therefore, the three points are: QUOTE, QUOTE, and QUOTE.

The equation for the parabola can be obtained using those three points. The parabola is centered, so the x-term is not added to or subtracted from before being multiplied by its coefficient. The parabola must also be negative to create the necessary shape. Using the y-intercept, we can create the preliminary equation QUOTE, where a is a coefficient that must be solved for. To do this, we use an x-intercept. Thus:

To find the width of the channel through which the tanker can pass, one must find the length of the value of x when the parabola is intersected by the horizontal line QUOTE. Hence:

Hence, the parabolic bridge allows 234.287 ft of clearance from the centerline, or about 470 ft in all.

The equation for the ellipse is found in…… [read more]


Observation of Phenomenon Aurora Borealis and Mammatus Clouds Essay

Essay  |  2 pages (534 words)
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¶ … Natural Phenomena

Observing the Aurora Borealis

The Aurora Borealis phenomenon is breathtaking to watch, both aesthetically as well as conceptually and philosophically. At the simplest level, it emits color schemes that are not typically seen in the atmosphere. Second, it produces types of apparent motion that are sometimes seen in a fluid medium on earth, but rarely elsewhere, especially in the sky overhead.

My initial thoughts while watching the Aurora Borealis had to do with the monumental significance such phenomena would naturally have represented to ancient people. There is lifelikeness to the horizontal movement of the phenomenon that would suggest a consciousness to ancient observers with the capacity of human intellectual curiosity. It is almost inconceivable that ancient observers would have attributed the lightshow to anything other than some sort of Divine demonstration of power. The phenomenon also makes me more aware of the sheer range of atmospheric manifestations that are possible. In that respect, it serves as a reminder that the phenomena we see on a regular basis are only a small portion of the range of possibilities. My observation also reminded me that it is probably the case that the atmospheric phenomena of every planet large enough to have an atmosphere are unique to that planet.

However, my most overwhelming reaction to the Aurora Borealis is appreciation and awe at the human intellect for having the capacity to quantify such incredible natural phenomena in mathematical terms. It was while imagining how complex the formulas of Lorentz, Maxwell, Faraday, and other mathematicians and theoretical physicists who provided technical descriptions of the unimaginable. It was…… [read more]


Nonlinear Aerostatics Stability Analysis of Suspension Bridges Literature Review Chapter

Literature Review Chapter  |  10 pages (3,491 words)
Style: Harvard  |  Bibliography Sources: 5

SAMPLE TEXT:

Su, Luo & Yun (2010) performed an aerostatic reliability of bridges with long spans. According to their study, the response surface Monte Carlo method (RSMCM) is suggested to be suitable for the analysis of the reliability of both the aerostatic stability and the aerostatic response for various types of long-span bridge structures. In these bridges, the nonlinear effects that come… [read more]


New Knowledge on Which Decisions and Actions Essay

Essay  |  3 pages (944 words)
Bibliography Sources: 3

SAMPLE TEXT:

¶ … new knowledge on which decisions and actions can be founded (Hughes & Hayhoe 2007). Here, new knowledge is created through the collection and analysis of observations in a systematic way. Further, research concerns itself with the articulation of truths (generalized) from given instances. For instance, research on reader behavior looks at the behavior of readers in general and not a particular reader's behavior in isolation.

Basically, qualitative research concerns itself with clarifying human experience. Below are examples in which case qualitative research comes in handy as far as human experience is concerned.

Example 1: A study of how human beings relate with each other from the ages of 18 to 30.

Example 2: A study of how culture impacts on the performance of school going children.

Example 3: A study of the relationship between monetary compensation and employee motivation

Example 4: A study of the relationship between upbringing and child delinquency

Example 5: A study of how gay tendencies impact on an individual's interaction with members of the opposite sex.

Question 3

The process in this case (in relation to question 2) would be conduction of interviews which are categorized as a type of non-numerical data on which qualitative methods rely on. Therefore, interviews can be used as the source data while seeking to identify the meaning of experiences humans undergo.

Question 4

While inductive reasoning is mainly used in qualitative research, quantitative research makes use of deductive reasoning (Kumar 2011). That is, in quantitative research, the focus generally zeroes in on the specific rather than the general. However, in qualitative research, larger theories are inferred to by the use of small observations.

Question 5

By undertaking hypothesis testing of the research question given, I will be seeking to either prove or disprove the same. The checklist I would rely on in this case is outlined by Hughes & Hayhoe (2007).

I will first come up with the test hypothesis whilst ensuring that I single out both the dependent and the independent variable.

Secondly, to ensure that I remain focused on the test's primary concern, I will develop the null hypothesis from the test hypothesis.

Next, I will engage in data collection after which I will feed the data collected into separate columns of a spreadsheet.

I will then engage in sample size tallying (for each group) using the COUNT function and then compute each group's mean using the AVERAGE function. Next I will, compute each group's standard deviation using the function STDEV.

On computing the standard deviation, I will seek to find out the p value using the TTEST function.

The next step in this case will be to use the p value I computed in the previous step as the basis for null hypothesis acceptance or rejection. According to Hughes & Hayhoe (2007), the null hypothesis can typically…… [read more]


Math and Chosen Profession Essay

Essay  |  3 pages (936 words)
Bibliography Sources: 3

SAMPLE TEXT:

Math and Chosen Profession

When most people think about the careers of firefighters and paramedics, they will often associate it with physically going into dangerous places to save lives. A good example of this can be seen with the heroic roles of many paramedics and firefighters after the 911 terrorist attacks. In these situations, they were demonstrating visceral force and determination during the course of doing their jobs. However, there is also a mental aspect of these career fields that must be taken into account. To fully understand what is happening requires looking at: how Algebra and the Metric system are utilized as part of their daily responsibilities. Together, these elements will provide the greatest insights as to the role of both areas for these career fields. ("911 Memorial for America's Heroes," 2007) (Monteclavo, 2011)

Describe how the Concept can apply to Firefighters and Paramedics

In both jobs there is a heavy reliance on using Algebra and the Metric system in conjunction with each other. For firefighters, this will occur through utilizing these areas when determining the right amounts of foam, water pressure and oxygen that is available. This will have a direct impact on their ability to quickly extinguish the blaze. (Monteclavo, 2011)

Paramedics must be able to use Algebra to make quick conversions when dealing with drugs and other medication. At the same time, they have to accurately work between the English and the Metric systems. These two factors can have an impact on the ability of paramedics to stabilize the patient (which increases their chances of survival). (Monteclavo, 2011)

Describe how to use Algebra / the Metric System and Provide Examples of Situations

Like what was stated previously, both career fields are dependent upon the use of Algebra and the Metric system in correlation with each other. In the case of firefighters, this is an everyday part of the job that requires them to make mathematical calculations instantaneously. This will determine how quickly they are able to fight the fire and save lives. (Monteclavo, 2011)

For example, during the course of a fire, the crews will use Algebra and the Metric system to decide how much water should be delivered to a particular area. As the flames are reacting to the water, is when these conversions will have to be adjusted higher and lower. In most cases this involves using Algebra to predict the right amount of pressure. At the same time, Algebra must be utilized to convert between the English and the Metric systems. This is illustrating how all firefighters will use both Algebra and the Metrics system to decide the best way to fight fires. (Monteclavo, 2011)

In the case of paramedics, the must use Algebra and the Metric system during the course of their daily activities. A good example of this can…… [read more]


Z Score Fill in the Answers Term Paper

Term Paper  |  6 pages (1,646 words)
Bibliography Sources: 10

SAMPLE TEXT:

Z Score

Fill in the answers for each table and answer the concluding FOUR questions below. Please round up your z scores to the hundredths spot, two decimals to the right and p values to the thousandths spot three decimals to the right as needed. If the p value is less than .001, please report p < .001. Please note… [read more]


Personality Impressions Term Paper

Term Paper  |  4 pages (1,195 words)
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SAMPLE TEXT:

Burkard, Alan W. And Knox, Sarah (2004). Effect of therapist color blindness on empathy and attributions in cross-cultural counseling. Journal of Counseling Psychology, 51:4, 387-397.

Whether research investigations are designed on the basis of an experimental, descriptive, historical, or case study format there must exist a clearly defined research question which informs the reader as to the specific intent of the research undertaken. When the research design is experimental or descriptive there must follow a well-formulated testable null hypothesis. Should these two research tenets not be in place then the research is said to be ad hoc and of little useful propose with respect to the validity and reliability of content knowledge. The present article reviewed and authored by Burkard and Knox (2004) can be best described as ad hoc research and did not follow the best-fit practice for effective research. The reasons for this summary statement is based upon the following reasons:

research question is to be presented at the beginning of a research investigation and if designed as an experimental of descriptive study a testable null hypothesis (es) follows. Buckard and Knox did not formally present a research question and the hypotheses presented were not only directional and non-testable (i.e., null form) but also highly biased as well: "...we hypothesized that those therapists were higher in color blindness racial attitudes..." "...we predicted that therapists' color blindness would be related to...." "..we predicted therapists' color blind racial attitudes would..." (p. 389). Continuing one step further, the research investigators failed to even alert the reader as to the research problem even though they presented a great deal of information pertaining to the overall area of study. At no time is a research investigator permitted to pre-formulate a direction that a sequence of events might take. All that a research is permitted to do is hypothesize that no differences, effects, or relationships will be uncovered as a result of the investigation. The reason being is that without a testable null hypothesis a research investigator cannot explain why something some thing did happen, and not why something did not happen. Therefore a research investigator must always begin with a statement (null hypothesis) that something will not happen.

With respect to the sample used in the study the authors failed to alert the reader as to the randomness of selection. When samples are chosen on the basis of non-randomization, the statistical tool chosen to analyze the day must be "re-fitted" to accommodate for non-randomization of selection.

The data analysis discussed in the report (p. 391-393) makes reference to an ANOVA and Pearson "r" coefficient analysis. These two particular statistical tools are employed to determine effects/differences and relationships between and amongst the variables under investigation. As there exists no rationale for seeking differences or effects the use of the ANOVA technique is circumspect. For there to exist legitimacy for the use of the ANOVA technique the reader should have been presented a testable null hypothesis stating effects and/or differences between and amongst the variables… [read more]

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