The population mean waiting time to check out of a supermarket has been 10.73 minutes. Recently, in an effort to reduce the waiting time, the supermarket has experimented with a system in which there is a single waiting line with multiple checkout servers. A sample of 100 customers was selected, and their mean waiting time to check out was 9.52 minutes, with a sample standard deviation of 5.8 minutes.
a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 10.73 minutes?
b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 10.73 minutes?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b).