XR18-76 The head office of a life insurance company believed that regional managers should have…

XR18-76 The head office of a life insurance
company believed that regional managers should have weekly meetings with their
salespeople, not only to keep them abreast of current market trends but also to
provide them with important facts and figures that would help them with their
sales. Furthermore, the company felt that these meetings should be used for pep
talks. One of the points managements felt strongly about was the high value of
new contact initiation and follow-up phone calls. To dramatize the importance
of phone calls on prospective clients and (ultimately) on sales, the company
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XR18-76 The head office of a life insurance
company believed that regional managers should have weekly meetings with their
salespeople, not only to keep them abreast of current market trends but also to
provide them with important facts and figures that would help them with their
sales. Furthermore, the company felt that these meetings should be used for pep
talks. One of the points managements felt strongly about was the high value of
new contact initiation and follow-up phone calls. To dramatize the importance
of phone calls on prospective clients and (ultimately) on sales, the company
undertook the following small study. Twenty randomly selected life insurance
salespeople were surveyed to determine the number of weekly sales calls they
made and the number of policy sales they concluded. The data partly shown in
the following table were collected and stored.

a Find the least squares regression line
that expresses the number of sales as a function of the number of calls.

b What do the coefficients tell you?

c Is there enough evidence (with _ =
0.05) to indicate that the larger the number of calls, the larger the number of
sales?

d What proportion of the variability in the
number of sales can be attributed to the variability in the number of calls?

e Find a 90% confidence interval estimate
of the mean number of sales made by all the salespeople who each make 50 calls.

f Predict with 99% confidence the number of
sales concluded by a salesperson who makes 30 calls.

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