A 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 are shown. Complete parts (a) through (f) below.
|
City
Test Cities
|
Percent Change in
Average Market Share per Month
|
|---|
1
|
+8 |
|
|---|
2
|
|
3
|
|
4
|
|
Control Cities
+2
|
1
|
|
|---|
2
|
|
3
|
|
4
|
0
|
(a) Find the mean of the change in market share for the four test cities.
The mean is ____ (Type an integer or decimal rounded to two decimal places as needed.)
(b) Find the mean of the change in market share for the four control cities.
The mean is ____ (Type an integer or decimal rounded to two decimal places as needed.)
(c) Find the standard deviation of the change in market share for the four test cities.
The standard deviation is ____ (Type an integer or decimal rounded to two decimal places as needed.)
(d) Find the standard deviation of the change in market share for the four control cities.
The standard deviation is _____ (Type an integer or decimal rounded to two decimal places as needed.)
(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.
The difference is _____ (Type an integer or decimal rounded to two decimal places as needed.)
(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? _______
(Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.)