7.128 Average service time. Recall the drive-thru study in Exercise 7.69 (page 457). Another benchmark that was measured was the service time. A summary of the results (in seconds) for two of the chains is shown below.
| Chain | n | s | |
|---|---|---|---|
| Taco Bell | 308 | 158.03 | 33.8 |
| McDonald’s | 317 | 189.49 | 41.3 |
(a) Is there a difference in the average service time between these two chains? Test the null hypothesis that the chains’ average service time is the same. Use a significance level of 0.05.
(b) Construct a 95% confidence interval for the difference in average service time.
(c) Lex plans to go to Taco Bell and Sam to McDonald’s. Does the interval in part (b) contain the difference in their service times that they’re likely to encounter? Explain your answer.