Question

1. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether or not the customer left a tip.19 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.

2. A sample of 40 runners will be used to compare two new routines for stretching. The runners will be randomly assigned to one of the routines which they will follow for two weeks. Satisfaction with the routines will be measured using a questionnaire at the end of the two-week period. For the first routine, nine runners said that they were satisfied or very satisfied. For the second routine, six runners said that they were satisfied or very satisfied.

a) For each scenario, find the large-sample 95% confidence interval for the difference in proportions and use the scenario to explain the meaning of the confidence interval.

b) For each scenario, perform the large-sample significance test and use the scenario to explain the meaning of the significance test.

Answer 1

#1 Let be the proportion of customer left a tip wearing a red shirt and be the proportion of customer left a tip wearing different colored shirt.

The hypotheses are:

Given .

The sample proportions are:

The pooled proportion is:

The test statistic is:

For two tailed test, the p-value is:

Since p-value < 0.05, reject the null hypothesis. We can conclude that there is a relationship between the color of the shirt worn by the server and whether or not the customer left a tip.