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In this problem, n=38, x-bar = 28.7 minutes, s = 3.8 minutes. a. A points estimate of the mean time required to handle a customer complaint = 28.7 minutes.
b. the standard deviation of the point estimate or the standard error = 3.8/sqrt(38) = 0.61644
c. The critical value that corresponds to confidence level of 95% and degree of freedom of 37 is 2.026. Then, the 95% confidence interval is 28.7 +/- 2.026*0.61644 = 28.7 +/- 1.2489 = (27.451, 29.949)
It means the office manager is 95% confident that the mean time for handling a complaint is between 27.45 minutes and 29.949 minutes.
Please let me know if you have any questions related to this problem.
May I know how I can assist you in understanding this question better?
Confidence interval for a mean is calculated as point estimate +/- margin of error. From part a, we have the point estimate of 28.7 minutes. The margin of error = critical value * standard error. Part b, we got the standard error as 0.61644. Part c, we have the critical value as 2.026. That means the margin of error = 2.026*0.61644 = 1.2489. Putting everything together, the 95% confidence interval = (28.7-1.2489, 28.7+1.2489) = (27.451, 29.949)
Please let me know if you need further explanation.