Chapter 9.2, Problem 26E

Sales Promotion The Quaker Oats Company conducted a survey to determine whether a proposed premium, to be included in boxes of cereal, was appealing enough to generate new sales. Four cities were used as test markets, where the cereal was distributed with the premium, and four cities as control markets, where the cereal was distributed without the premium. The eight cities were chosen on the basis of their similarity in terms of population, per capita income, and total cereal purchase volume. The results were as follows. Source: Quaker Oats Company.

City		Percent Change in Average Market Share per Month
	1	+ 18
	2	+ 15
Test Cities
	3	+7
	4	+ 10
	1	+ 1
	2	–8
Control Cities
	3	–5
	4	0

(a) Find the mean of the change in market share for the four test cities.

(b) Find the mean of the change in market share for the four control cities.

(c) Find the standard deviation of the change in market share for the test cities.

(d) Find the standard deviation of the change in market share for the control cities.

(e) Find the difference between the means of parts (a) and (b). This difference represents the estimate of the percent change in sales due to the premium.

(f) The two standard deviations from parts (c) and (d) were used to calculate an "error" of ±7.95 for the estimate in part (e). With this amount of error, what are the smallest and largest estimates of the increase in sales?

On the basis of the interval estimate of part (f), the company decided to mass-produce the premium and distribute it nationally.