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 μ 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 μ is shorter than six minutes.
b. The mean and the standard deviation of the sample of 100 bank customer waiting times are  = 5.46 and s = 2.475. Use a critical value to test the hypotheses you set up in part (a) by setting a equal to .05. Also, interpret the p-value of .0158 for the hypothesis test.