# Sampling, Regression, and Hypothesis Testing Statistical Analysis

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2 · **File:** .docx · **Level:** College Junior · **Topic:** Education · **Written:** July 14, 2019

SAMPLE EXCERPT:

[. . .] In reality, both Type 1 and Type II errors can be severe. Type I error is unavoidable because every time we reject the null hypothesis, there is a high possibility we have made such an error. This error is costly because Pfizer will incur unnecessary costs developing and marketing Drug B. On the other hand, Type II error may lead to Pfizer abandoning further research on Drug B, which could have generated high profits for the company because it is more effective than Drug A.

11.

a. The null hypothesis is: = 6 (the mean volume of bottles is equal to 6 ounces).

The alternative hypothesis is: 6 (the mean volume of the bottles is not equal to 6 ounces).

b. The formula for calculating test statistic. Using cough syrup data = 5.989 and = = = 0.094868. Therefore, the value of test statistic is

c. Using Excel in-built function NORMDIST, p-value is 0.9707.

d. The sample data is consistent with the null hypothesis that the mean volume of bottles is equal to 6 ounces. Therefore, the hypothesis test does not provide sufficient evidence to support the claim that bottles are inadequately filled.

12. The formula for calculating Z score is where = population mean and = population standard deviation. Therefore, the value of Z score is

13. Using standard normal probabilities table, P (z = 0.8824) = 0.3776. It means that there is a 37.76% likelihood that a value greater than 17 will occur by chance.

14. The value of Z score is

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for $19.77 Using standard normal probabilities table, P (z > -1.05) = .8531. It means that 85.31% of babysitters are paid more than $12 per hour.

P (z < -1.05) = .1469. It means that 14.69% of babysitters are paid less than $12 per hour.

Based on the above findings, I will give the babysitter a pay rise because approximately 85% of the babysitters are earning more than her on average. If I fail to increase her pay, she might resign.

15.

a. : The average SAT math scores of students who completed the tutoring program is 399.

## Statistical Analysis on

: The average SAT math scores of students who completed the tutoring program is less than 399.

The Z score value is

P (z = -4.00) = 3.16712 . Since the p-value = 3.16712 < 0.01, we reject the null hypothesis and conclude that Tutor O-Rama claim is inaccurate at 1% significant level.

b. : The average SAT math score is 350 and: The average SAT math score is less than 350.

The Z score value is

P (z = -4.00) = 1. Since the p-value is greater than 0.01 and 0.05, we reject the null hypothesis and conclude the average SAT math score is less than 350 at 95% confidence level as well as 99% confidence level.

Definitions

Application of Regression

Regression analysis is used in forecasting and to determine the relationship that exists between economic variables. For example, regression can be used to determine the relationship that exists between income and consumption. Regression can also be used to predict (forecast) the value of future sales given sales data.

Conclusion

This course has improved my statistical reasoning because I can apply various statistical concepts such as hypothesis tests and regression when analyzing quantitative data.… [END OF PREVIEW] . . . READ MORE

[. . .] In reality, both Type 1 and Type II errors can be severe. Type I error is unavoidable because every time we reject the null hypothesis, there is a high possibility we have made such an error. This error is costly because Pfizer will incur unnecessary costs developing and marketing Drug B. On the other hand, Type II error may lead to Pfizer abandoning further research on Drug B, which could have generated high profits for the company because it is more effective than Drug A.

11.

a. The null hypothesis is: = 6 (the mean volume of bottles is equal to 6 ounces).

The alternative hypothesis is: 6 (the mean volume of the bottles is not equal to 6 ounces).

b. The formula for calculating test statistic. Using cough syrup data = 5.989 and = = = 0.094868. Therefore, the value of test statistic is

c. Using Excel in-built function NORMDIST, p-value is 0.9707.

d. The sample data is consistent with the null hypothesis that the mean volume of bottles is equal to 6 ounces. Therefore, the hypothesis test does not provide sufficient evidence to support the claim that bottles are inadequately filled.

12. The formula for calculating Z score is where = population mean and = population standard deviation. Therefore, the value of Z score is

13. Using standard normal probabilities table, P (z = 0.8824) = 0.3776. It means that there is a 37.76% likelihood that a value greater than 17 will occur by chance.

14. The value of Z score is

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for $19.77 Using standard normal probabilities table, P (z > -1.05) = .8531. It means that 85.31% of babysitters are paid more than $12 per hour.

P (z < -1.05) = .1469. It means that 14.69% of babysitters are paid less than $12 per hour.

Based on the above findings, I will give the babysitter a pay rise because approximately 85% of the babysitters are earning more than her on average. If I fail to increase her pay, she might resign.

15.

a. : The average SAT math scores of students who completed the tutoring program is 399.

## Statistical Analysis on *Sampling, Regression, and Hypothesis Testing* Assignment

: The average SAT math scores of students who completed the tutoring program is less than 399.The Z score value is

P (z = -4.00) = 3.16712 . Since the p-value = 3.16712 < 0.01, we reject the null hypothesis and conclude that Tutor O-Rama claim is inaccurate at 1% significant level.

b. : The average SAT math score is 350 and: The average SAT math score is less than 350.

The Z score value is

P (z = -4.00) = 1. Since the p-value is greater than 0.01 and 0.05, we reject the null hypothesis and conclude the average SAT math score is less than 350 at 95% confidence level as well as 99% confidence level.

Definitions

- Simple linear regression is a linear regression model with only one explanatory (independent) variable.
- A simple linear regression has only one explanatory variable while a multiple regression has more than one explanatory variable.
- A dependent variable refers to a variable that is being measured in an experiment while an independent variable is a variable that explains the changes in the dependent variable. The dependent variable is the y-variable while the independent variable is the x-variable.

Application of Regression

Regression analysis is used in forecasting and to determine the relationship that exists between economic variables. For example, regression can be used to determine the relationship that exists between income and consumption. Regression can also be used to predict (forecast) the value of future sales given sales data.

Conclusion

This course has improved my statistical reasoning because I can apply various statistical concepts such as hypothesis tests and regression when analyzing quantitative data.… [END OF PREVIEW] . . . READ MORE

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