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 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. In the context of this situation, interpret making a Type I error; interpret making a Type II error.