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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
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.
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