Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes. Suppose the manager wishes to use the random sample of 100 waiting times to support the claim that the mean waiting time under the new system is shorter than six minutes.

a. Letting m represent the mean waiting time under the new system, set up the null and alternative hypotheses needed if we wish to attempt to provide evidence supporting the claim that m is shorter than six minutes.

b. The random sample of 100 waiting times yields a sample mean of 5.46 minutes. Assuming that the population standard deviation equals 2.47 minutes, use critical values to test H0 versus Ha at each of α = .10, .05, .01, and .001.

c. Using the information in part b, calculate the p-value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001.

d. How much evidence is there that the new system has reduced the mean waiting time to below six minutes?