A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes that the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes. Suppose that the manager wishes to use 100 waiting times to support the claim that the mean waiting time under the new system is shorter than six minutes. The random sample of 100 waiting times yields a sample mean of 5.46 minutes. Further, let's assume that the population standard deviation is 2.475.

a) State the null and alternative hypotheses, letting u represent the mean waiting time under the new system.

b) Select the distribution to use. Explain briefly why you selected it.

c) Assuming that she wishes to test the claim at alpha = 0.05, determine the rejection and non-rejection regions based on your hypotheses in (a). State the critical value.

d) Calculate the value of the test statistic.

e) What do you conclude about whether the new system has reduced the mean waiting time to below six minutes? Explain your conclusion in words.