Recall that a bank manager has developed a new system to reduce the time custome
ID: 3219916 • Letter: R
Question
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served 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 99 bank customer waiting times is x bar = 5.44. If we let mu denote the mean of all possible bank customer waiting times using the new system and assume that sigma equals 2.48: (a) Calculate 95 percent and 99 percent confidence intervals for mu. 95 percent confidence intervals for mu is [, ] 99 percent confidence intervals for mu is [, ] (b) Using the 95 percent confidence interval, can the bank manager be 95percent confident that mu is less than six minutes? Explain. 95% interval is 6. (c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that mu is less than six minutes? Explain. 99% interval extends 6. (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? confident since 95% Cl is 6 while 99% Cl contains 6.Explanation / Answer
(a)
(i) 95% CI
n = 99
x-bar = 5.44
s = 2.48
% = 95
Standard Error, SE = /n = 0.2492
z- score = 1.9600
Width of the confidence interval = z * SE = 0.4885
Lower Limit of the confidence interval = x-bar - width = 4.951471
Upper Limit of the confidence interval = x-bar + width = 5.928529
The confidence interval is [ 4.951 5.929]
(ii) 99% CI
n = 99
x-bar = 5.44
s = 2.48
% = 99
Standard Error, SE = /n = 0.2492
z- score = 2.5758
Width of the confidence interval = z * SE = 0.641889
Lower Limit of the confidence interval = x-bar - width = 4.798111
Upper Limit of the confidence interval = x-bar + width = 6.081889
The confidence interval is [ 4.798 6.082]
(b)
Yes, the entire 95% CI is less than 6.
Therefore, the manager can be 95% confident that is less than 6 minutes.
(c)
No, a small part of the 99% CI is greater than 6.
Therefore, the manager can’t be 99% confident that is less than 6 minutes.
(d)
At = 0.05, we are convinced that the mean waiting time is less than 6 minutes, but not at = 0.01.
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