Is there evidence that the population mean waiting time is less than 5 minutes?

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1:00 P.M. lunch period. The waiting time (defined as the time the customer enters the line until he or she reaches the teller window) of all customers during this hour is recorded over a period of 1 week. A random sample of 15 customers is selected, and the results are as follows:
4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79
a. At the 0.05 level of significance, is there evidence that the population mean waiting time is less than 5 minutes?
b. What assumption about the population distribution is needed in order to conduct the t test in (a)?
c. Use a boxplot or a normal probability plot to evaluate the assumption made in (b).
d. Do you think that the assumption needed in order to conduct the t test in (a) is valid?
e. As a customer walks into the branch office during lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies “Almost certainly not longer than 5 minutes.” On the basis of the results of (a), evaluate this statement.

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