The manager of a supermarket would like the variance of the waiting times of the customers not to exceed 3 minutes squared. She would add a new cash register if the variance exceeds this threshold. She regularly checks the waiting times of the customers to ensure that the variance does not rise above the allowed level. In a recent random sample of 28 customer waiting times, she computes the sample variance as 4.2 minutes-squared. She believes that the waiting times are normally distributed.
a. State the null and the alternative hypotheses to test if the threshold has been crossed.
b. Use the p-value approach to conduct the test at α = 0.05.
c. Repeat the analysis with the critical value approach.
d. What should the manager do?