9. Marketing: Coupons Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healthy Crunch has a policy of answering all its mail on the day it is received.)

Let x 5 weight of incoming mail and y 5 number of employees required to process the mail in one working day. A random sample of 8 days gave the following data:

x (lb) 11 20 16 6 12 18 23 25 y (Number of employees) 6 10 9 5 8 14 13 16

©x 5 131; ©y 5 81; ©x2 5 2435; ©y2 5 927; ©xy 5 1487

(a) Draw a scatter diagram for the data.

(b) Find x, y,

b, and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination.

What percentage of the variation in y is explained by the leastsquares model?

(d) Test the claim that the population correlation coefficient r is positive at the 1% level of significance.

(e) If Healthy Crunch receives 15 pounds of mail, how many employees should be assigned mail duty that day?

(f) Verify that Se < 1.726.

(g) Find a 95% confidence interval for the number of employees required to process mail for 15 pounds of mail.

(h) Test the claim that the slope b of the population least-squares line is positive at the 1% level of significance.

(i) Find an 80% confidence interval for b and interpret its meaning.