# Statistical Analysis of Restaurant PatronsTerm Paper

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Statistical Analysis of Restaurant Patrons

What type of research question (ie: descriptive, comparative, relationship) is being asked by the researchers?

The research question being asked by the researchers is that of comparing the expression on a patrons' face in a restaurant being a predictor of the percentage of tip given to their waiter or waitress. The researchers are using a comparative model to see if there are statistically significant differences between those groups that do not exhibit a happy face, as designated by the variable name NHF (No Happy Face) versus those patrons who exhibit a happy face (HF). The intent of this analysis is to see if there is a significant difference between the control group in this analysis (which is the NHF group) versus the HF group of customers. The HF group of customers is the experimental group. There are a total of 44 data cases included in this analysis, divided into two groups of 22 each. The data is analyzed using SPSS Version 13.0 for Windows.

2. What were the independent and dependent variables in the study?

The independent variables are the expression of the patrons in the restaurant. As this is a comparative research design, the respondents are divided into the two variable groups of NHF and HF. The dependent variable in each of the two groups is the percentage of tips given by customers in the experimental and control groups, HF and NHF respectively.

3. What is the level of measurement for the independent and dependent variable?

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The data sets contain the percentage of tips given by both HF and NHF customers, which could be zero if no tip was given, are by definition at the ratio level of measurement. A ratio level measurement is one that has an absolute zero, and since any patron in the sample could not have tipped at all, the ratio level of measurement applies to the data. For a description of all levels of measurement please see the reference provided (ResearchMethods 2007).

## Term Paper on Statistical Analysis of Restaurant Patrons What Type Assignment

4. Before performing data analysis, make predictions about the pattern of results you expect to see and why. That is, which condition do you think will result in the highest percentage of tips, on average? Why? Note: do not base your prediction on the data itself, rather on the expectations going into the study. That is, before you collect any data, what you expect to see?

Common sense dictates that the HF group will be the one with the higher relative and absolute levels of tips as a percentage of their total dining bills. The NHF group, whether the expression on the respondents' faces is from thoughts pertaining to events and circumstances completely unrelated to the restaurant, or conversely the restaurants' atmosphere, service or food quality, naturally would be assumed to deliver lower tips. One could also assume that the HF groups of respondents are more optimistic about their lives and situations they encounter vs. The NHF group, which appear, from their expressions, to be focused on other thoughts or not enjoying the experience of being in the restaurant.

5. Calculate the mean, median, and mode and the standard deviation for the experimental group using SPSS.

As the HF group has been defined as the experimental group, and presented below are the summary of Statistical Analysis using the Frequencies Command in SPSS Version 13 for Windows:

Statistics

Tip percentage for happy face (smiling) patrons

Valid

Missing

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Kurtosis

Std. Error of Kurtosis

Range

Minimum

Maximum

Sum

Percentiles

Multiple modes exist. The smallest value is shown

Also shown below is a histogram of the experimental variable, HF. Figure 1: Histogram of the HF Variable (Experimental Group) shows graphically the distribution of tip percentages, with the mean value being 33.0455 and the standard deviation being 13.95393.

Figure 1: Histogram of the HF Variable (Experimental Group)

6. Explain in a sentence or two, the standard deviation value in the previous question.

In such a small sample size (n=22) the standard deviation of 13.95393 shows a very high level of variability in the data. Plotting the data into a histogram and completing curve fitting to the data shows that the data set is nearly bifurcated into two separate levels of tipping in the HF group.

7. Compare the means for the two groups. Does the pattern of the mean differences match your prediction from question #4?

The mean value for the NHF group is 27.5 and the HF group is 33.0455. Using means alone does show that the NHF group did in fact tip less than the HF group. Yet comparing means alone does not support the specific assumption of HF group patrons tipping higher, there is additional analysis needed to prove this hypothesis.

Inferential Statistics Questions:

8. Write null and alternate hypothesis

Null Hypothesis: The HF group will not give a higher percentage of tips due to their apparent satisfaction with the dining experience.

Alternative Hypothesis: The HF group will give a higher percentage of their bills as a tip based on their apparent satisfaction with the dining experience.

9. One of the assumptions of the independent T test is homogeneity of variance. Explain the assumptions; explain the use of the Levene's test in the T test.

The key assumptions of Levene's Test for Equality of Variances include the following:

There will be equal variances across samples, which is often referred to in the context of Levene's Test of Equality as measuring for the homogeneity of variance.

Testing variation between means at the 95% confidence interval is relied on for rejecting the Null Hypothesis and accepting the Alternative Hypothesis.

The Levene Test for Equality of Variances also assumes that the randomness of each group being tested for homogeneity of variance are random, and also have a fixed scale. In the case of measuring the percentage of tips given by respondent groups HF and NHF, it has been mentioned earlier that the data is ratio-level of robustness given it can have an absolute zero value (no tip given at all).

10. Obtain the appropriate test statistics from the SPSS menus choose Analyse and Compare Means, followed by the appropriate test. What is the value of the t statistic and probability value on the SPSS printout?

When completing the analysis using the Paired Samples T-Test where both HF and NHF are included in the analysis yields a t-score of -3.402. Completing a Measures of Association analysis yields an R2 of.817, showing that both groups a very high level of correlation between both groups.

Measures of Association

Squared

Eta

Eta Squared

Tip percentage for happy face (smiling) patrons * Tip percentage for non-happy face patrons

11. What is your decision concerning the null hypothesis? Did you reject or retain? Provide a rationale.

Accept the Null Hypothesis of the HF group not giving a higher percentage of tips due to their apparent satisfaction with the dining experience based on an analysis of variances between the experimental and control groups. An analysis of means and standard deviations supports the acceptance of the Null Hypothesis, showing that despite the NHF group intuitively not likely to leave bigger tips, they in fact did with much less variation in the percentage of the dining bill given as a tip to servers.

12. What are some variables unaccounted for that may have impact on the results? Write this paragraph in terms of potential limitations of your results.

There are many variables that could potentially impact the level of gratuity or tip left by patrons to a restaurant. Starting with an assessment of the quality of service including how long the patron had to wait to be seated, served their dinner, and if the waiter or waitress was attentive and responsive during the dining experience are… [END OF PREVIEW] . . . READ MORE

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