A bank located in a commercial district of a city had the business objective of improving the process for serving customers during the noon-to-1:00PM 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 a week. Data were collected from a random sample of 15 customers, and the results are organized 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) Do you think that the assumption needed in order to conduct the t test in a) is valid? Explain.
d) As a customer walks to the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, “About certainly not longer than 5 minutes”. On the basis of the results of a), evaluate this statement.