Question

1. Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the 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 1.9 is 5.46. If we let μ denote the mean of all possible bank customer waiting times using the new system and assume that the population standard deviation equals 2.47:

1. Calculate 95 percent and 99 percent confidence intervals for μ.
2. Using the 95 percent confidence interval, can the bank manager be 95 percent confident that μ is less than six minutes? Explain.
3. Using the 99 percent confidence interval, can the bank manager be 99 percent confident that μ is less than six minutes? Explain.
4. Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?

Answer 1

b)

Using the 95% confidence interval, the bank manager could be 95% confident that population mean is less than 6 minutes due to a 95% C.I. for population mean waiting time is between 4.824 to 5.944 does not include 6 minutes

c)

Using the 99% confidence interval, the bank manager could not be 99% confident that population mean is less than 6 minutes due to a 99% C.I. for population mean waiting time is between 4.976 to 6.096 does include 6 minutes

d)

Based on the answers of parts (b) and (c), it is fairly convinced that the new mean waiting time is less than 6 minutes, since 95% confidence interval is below 6 while 99% confidence interval contains 6