The amount of time a customer waits for service at a bank is normally distributed. While the manager believes that the waiting time for customers is at most 3 minutes on average, a customer claims that the average waiting time is at least 3.5 minutes. You selected a random sample of 16 customers and obtained a mean of 3.10 minutes and a standard deviation of 0.40 minutes for their wait times.
a) A null and alternate hypotheses to test the manager's belief (i.e., the waiting time for the customers is at most 3 minutes on average).
b) Using a significance level of 0.05, test the above hypotheses and draw a conclusion using a critical value (classical method) approach. (show all work).
c) Test the customer's claim (i.e., the average waiting time is at least 3.5 minutes) and draw a conclusion about the claim using a = 0.10. (show all work).