A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical waiting times during peak business hours under the current system are roughly 9 to 10 minutes. The bank manager hopes that the new system will lower typical waiting times to less than 6 minutes and wishes to evaluate the new system. When the new system is operating consistently over time, the bank manager decides to select a sample of 100 customers that need teller service during peak business hours. Specifically, for each of 100 peak business hours, the first customer that starts waiting for teller service at or after a randomly selected time during the hour will be chosen. Required:
a. Calculate 95 percent and 99 percent confidence intervals for μ.
b. Using the 95 percent confidence interval, can the bank manager be 95 percent confident that μ is less than six minutes? Explain.
c. Using the 99 percent confidence interval, can the bank manager be 99 percent confident that u is less than six minutes? Explain.
d. Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?