Recall that the bank manager has developed new system to reduce the time customers spend waiting to be served by the tellers throughout peak business hours. The mean time throughout peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting times in Table 1.8 is 5.46. If we let u denote mean of all possible bank customer waiting times using the new system and assume that standard deviation equals 2.47:
(a) Compute 95 percent and 99 percent confidence intervals for u.
(b) Using the 95 percent confidence interval, can the bank manager be 95 percent confident that u is less than six minutes? Discuss.
(c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that u is less than six minutes? Discuss.
(d) Based upon your answers to parts b and c, how convinced are you that new mean waiting time is less than six minutes?