Question

A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1:00 P.M. lunch period. The waiting time, in minutes, is defined as the time the customer enters the line to when he or she reaches the teller window. Data are collected from a sample of 15 customers during this hour. The following is the list of time data gathered from the bank branch in the commercial district. 4.31 5.45 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.20 0.38 5.12 6.46 6.19 3.89 At the 0.05 level of significance, is there evidence that the population mean waiting time is less than 5 minutes?

Answer 1

From the given data,

Now,

As population variance is not given, the test statistic is given by

Assuming null hypothesis is true, the test statistic is

Now, t_{​​​​​​14,0.05} is -1.761.

As the test statistic is not less than the critical value, thus we do not have sufficient evidence to reject null hypothesis.

Thus, we do not have sufficient evidence to say that the population mean waiting time is less than 5 minutes.