Question: The manager of a supermarket would like the variance of the waiting time soft the customers not to exceed 3minutes 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 its variance does not rise above the a l lowed 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 norm ally distributed.
a. State the null and the alternative h y p o theses 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?