Question

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.

x (lb)	14	23	17	6	12	18	23	25
y (Number of employees)	7	11	9	5	8	14	13	16

In this setting we have Σx = 138, Σy = 83, Σx² = 2672, Σy² = 961, and Σxy = 1581.

(a) Find x bar, y bar, b, and the equation of the least-squares line. (Round your x and y to two decimal places. Round your least-squares estimates to four decimal places.)

x bar	=
y bar	=
b	=
ŷ	= _______	+ ____ x

(b) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r = _____
r2 =_____

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

(c) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find the P value =

(d) If Healthy Crunch receives 21 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to two decimal places.)

(e) Find S_e. (Round your answer to three decimal places.)

(f) Find a 95% for the number of employees required to process mail for 21 pounds of mail. (Round your answer to two decimal places.)

lower limit	_____employees
upper limit	_____employees

(g) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find the P value =

(h) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

lower limit _____
upper limit _____

Answer 1