The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort to reduce the waiting time, the supermarket has experimented with a system in which infrared cameras use body heat and in-store software to determine how many lanes should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 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 4 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 4 minutes?

c. Interpret the meaning of the p-value in this problem.

d. Compare your conclusions in (a) and (b).