Calculate 95 percent and 99 percent confidence intervals for µ . (Round your ans
ID: 3219696 • Letter: C
Question
Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 decimal places.)
Using the 95 percent confidence interval, can the bank manager be 95 percent confident that µ is less than six minutes? Explain.
Using the 99 percent confidence interval, can the bank manager be 99 percent confident that µ is less than six minutes? Explain.
Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?
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 is = 5.43. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume that equals 2.44:
Explanation / Answer
ans=
a)(i) 95% CI
n = 100
x-bar = 5.43
s = 2.44
% = 95
Standard Error, SE = /n = 0.2440
z- score = 1.96
Width of the confidence interval = z * SE = 0.4782
Lower Limit of the confidence interval = x-bar - width = 5.43-0.4782 = 4.9518
Upper Limit of the confidence interval = x-bar + width = 5.43+0.4782 = 5.9082
The confidence interval is [ 4.9518,5.9082]
(ii) 99% CI
n = 100
x-bar = 5.43
s = 2.44
% = 99
Standard Error, SE = /n = 0.2440
z- score = 2.5758
Width of the confidence interval = z * SE = 2.5758*2.44 =0.6285
Lower Limit of the confidence interval = x-bar - width = 5.43-0.6285 = 4.8015
Upper Limit of the confidence interval = x-bar + width = 5.43+0.6285 = 6.0585
The confidence interval is [ 4.8015 6.0585]
(b) Yes, the entire 95% CI is less than 6. 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. 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.