# Question

The following partial Excel add- in ( MegaStat) regression output for the service time data relates to predicting service times for 1, 2, 3, 4, 5, 6, and 7 copiers.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean time to service four copiers.

b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the time to service four copiers on a single call.

c. For this case: n = 11, b0 = 11.4641, b1 = 24.6022, and s 4.615. Using this information and a distance value (called Leverage on the add-in output), hand calculate (within rounding) the confidence interval of part a and the prediction interval of part b.

d. If we examine the service time data, we see that there was at least one call on which Accu-Copiers serviced each of 1, 2, 3, 4, 5, 6, and 7 copiers. The 95 percent confidence intervals for the mean service times on these calls might be used to schedule future service calls. To understand this, note that a person making service calls will (in, say, a year or more) make a very large number of service calls. Some of the person’s individual service times will be below, and some will be above, the corresponding mean service times. However, because the very large number of individual service times will average out to the mean service times, it seems fair to both the efficiency of the company and to the person making service calls to schedule service calls by using estimates of the mean service times. Therefore, suppose we wish to schedule a call to service five copiers. Examining the computer output, we see that a 95 percent confidence interval for the mean time to service five copiers is [130.753, 138.197]. Because the mean time might be 138.197 minutes, it would seem fair to allow 138 minutes to make the service call. Now suppose we wish to schedule a call to service four copiers. Determine how many minutes to allow for the service call.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean time to service four copiers.

b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the time to service four copiers on a single call.

c. For this case: n = 11, b0 = 11.4641, b1 = 24.6022, and s 4.615. Using this information and a distance value (called Leverage on the add-in output), hand calculate (within rounding) the confidence interval of part a and the prediction interval of part b.

d. If we examine the service time data, we see that there was at least one call on which Accu-Copiers serviced each of 1, 2, 3, 4, 5, 6, and 7 copiers. The 95 percent confidence intervals for the mean service times on these calls might be used to schedule future service calls. To understand this, note that a person making service calls will (in, say, a year or more) make a very large number of service calls. Some of the person’s individual service times will be below, and some will be above, the corresponding mean service times. However, because the very large number of individual service times will average out to the mean service times, it seems fair to both the efficiency of the company and to the person making service calls to schedule service calls by using estimates of the mean service times. Therefore, suppose we wish to schedule a call to service five copiers. Examining the computer output, we see that a 95 percent confidence interval for the mean time to service five copiers is [130.753, 138.197]. Because the mean time might be 138.197 minutes, it would seem fair to allow 138 minutes to make the service call. Now suppose we wish to schedule a call to service four copiers. Determine how many minutes to allow for the service call.

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