A cereal company wants to see which of two promotional strategies, supplying coupons in a local newspaper or including coupons in the cereal package itself, is more effective. (In the latter case, there is a label on the package indicating the presence of the coupon inside.) The company randomly chooses 80 Kroger's stores around the country—all of approximately the same size and overall sales volume—and promotes its cereal one way at 40 of these sites, and the other way at the other 40 sites. (All are at different geographical locations, so local newspaper ads for one of the sites should not affect sales at any other site.) Unfortunately, as in many business experiments, there is a factor beyond the company's control, namely, whether its main competitor at any particular site happens to be running a promotion of its own. The file P09_70.xlsx has 80 observations on three variables: Sales: number of boxes sold during the first week of the company's promotion Promotion Type:1 if coupons are in local paper, 0 if coupons are inside box Competitor Promotion:1 if main competitor is running a promotion, 0 otherwise a. Based on all 80 observations, (1) Calculate the difference in sample mean sales (promotion type 0 minus promotion type 1) between stores running the two different promotional types. Round your answer to one decimal place, if necessary. Indicate which sample mean is larger. (2) Calculate the standard error of this difference. Round your answer to two decimal places, if necessary. (3) Calculate the 90% confidence interval for the population mean difference. Round your answer to one decimal place, if necessary. If your answer is negative number, enter "minus" sign. Lower Limit Upper Limit
A cereal company wants to see which of two promotional strategies, supplying coupons in a local newspaper or including coupons in the cereal package itself, is more effective. (In the latter case, there is a label on the package indicating the presence of the coupon inside.) The company randomly chooses 80 Kroger's stores around the country—all of approximately the same size and overall sales volume—and promotes its cereal one way at 40 of these sites, and the other way at the other 40 sites. (All are at different geographical locations, so local newspaper ads for one of the sites should not affect sales at any other site.) Unfortunately, as in many business experiments, there is a factor beyond the company's control, namely, whether its main competitor at any particular site happens to be running a promotion of its own. The file P09_70.xlsx has 80 observations on three variables:
- Sales: number of boxes sold during the first week of the company's promotion
- Promotion Type:1 if coupons are in local paper, 0 if coupons are inside box
- Competitor Promotion:1 if main competitor is running a promotion, 0 otherwise
a. Based on all 80 observations,
(1) Calculate the difference in sample mean sales (promotion type 0 minus promotion type 1) between stores running the two different promotional types. Round your answer to one decimal place, if necessary.
Indicate which sample mean is larger.
(2) Calculate the standard error of this difference. Round your answer to two decimal places, if necessary.
(3) Calculate the 90% confidence interval for the population mean difference. Round your answer to one decimal place, if necessary. If your answer is negative number, enter "minus" sign.
Lower Limit | ||
Upper Limit |
b. Test whether the population mean difference is zero (the null hypothesis) versus a two-tailed alternative. State whether you should reject or fail to reject the null hypothesis.
the null hypothesis. The confidence interval this claim because it .
c. Test whether the population mean difference is zero (the null hypothesis) versus a two-tailed alternative, but now restrict the population to stores where the competitor is not running a promotion of its own. State whether you should fail to reject or reject the null hypothesis.
the null hypothesis. The confidence interval this claim because it .
d. Based on data from all 80 observations, can you accept the (alternative) hypothesis, at the 5% level, that the mean company sales drop by at least 30 boxes when the competitor runs its own promotion (as opposed to not running its own promotion)?
e. We often use the term population without really thinking what it means. For this problem, explain in words exactly what the population mean refers to. What is the relevant population?
The population is sales in the of a coupon promotional campaign run by Kroger's stores that, with respect to size and volume, are those in the sample.
![44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 3 4 65 66 印 68 69 70 71 72 73 74 75 75 7 78 79 80
63
64
67
76
77
172
206
188
185
171
175
207
209
207
181
222
197
166
189
178
167
210
228
241
167
189
191
224
151
220
202
220
184
205
216
201
208
187
197
197
195
200
ooo
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
oooo
1
0
0
1
1
1
HOOHOO
1
1
1
1
1
1
0
0
0
1
LLOHO
1
1
1
1
ooo110ooooo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60820f5e-4036-4029-9914-6fc5dcb2f780%2F8b4874c4-d89b-4541-9e8b-056ec8acfed7%2Fpliiao_processed.png&w=3840&q=75)
![Store
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
13
Sales Promotion Type
169
242
175
253
236
158
231
205
169
178
200
200
229
230
193
234
218
211
218
152
223
174
225
194
197
223
150
190
196
202
197
220
245
196
222
202
289
229
193
216
160
209
175
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
Competitor Promotion
1
0
1
0
0
1
0
1
1
TOTOO
1
0
1
0
0
1
OTOOOOH
0
0
1
HOLLO
1
0
1
1
0
1
1
0
OTO OTTO
1
0
0
1
0
1
0
0
1
0
1
0
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60820f5e-4036-4029-9914-6fc5dcb2f780%2F8b4874c4-d89b-4541-9e8b-056ec8acfed7%2Fvwgchhp_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)