# Question

The file P08_65.xlsx contains data on the first 100 customers who entered a two-teller bank on Friday. All variables in this file are times, measured in minutes.

a. Find a 95% confidence interval for the mean amount of time a customer spends in service with a teller.

b. The bank is most interested in mean waiting times because customers get upset when they have to spend a lot of time waiting in line. Use the usual procedure to calculate a 95% confidence interval for the mean waiting time per customer.

c. Your answer in part b is not valid! We made two implicit assumptions when we stated the confidence interval procedure for a mean:

(1) The individual observations come from the same distribution, and

(2) The individual observations are probabilistically independent.

Why are both of these, particularly (2), violated for the customer waiting times?

d. Following up on assumption (2) of part c, you might expect waiting times of successive customers to be auto-correlated, that is, correlated with each other. Large waiting times tend to be followed by large waiting times, and small by small. Check this with StatTools’s Autocorrelation procedure, under the Time Series & Forecasting/Autocorrelation menu item. An autocorrelation of a certain lag, say, lag 2, is the correlation in waiting times between a customer and the second customer behind her. Do these successive waiting times appear to be auto-correlated?

a. Find a 95% confidence interval for the mean amount of time a customer spends in service with a teller.

b. The bank is most interested in mean waiting times because customers get upset when they have to spend a lot of time waiting in line. Use the usual procedure to calculate a 95% confidence interval for the mean waiting time per customer.

c. Your answer in part b is not valid! We made two implicit assumptions when we stated the confidence interval procedure for a mean:

(1) The individual observations come from the same distribution, and

(2) The individual observations are probabilistically independent.

Why are both of these, particularly (2), violated for the customer waiting times?

d. Following up on assumption (2) of part c, you might expect waiting times of successive customers to be auto-correlated, that is, correlated with each other. Large waiting times tend to be followed by large waiting times, and small by small. Check this with StatTools’s Autocorrelation procedure, under the Time Series & Forecasting/Autocorrelation menu item. An autocorrelation of a certain lag, say, lag 2, is the correlation in waiting times between a customer and the second customer behind her. Do these successive waiting times appear to be auto-correlated?

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