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

Σx = 131; Σy = 81; Σx² = 2435; Σy² = 927; Σxy = 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 least squares 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 S_e ≈ 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.