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. 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. 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_76.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, find (1) the difference in sample mean sales between stores running the two different promotional types (and indicate which sample mean is larger), (2) the standard error of this difference, and (3) a 90% confidence interval for the population mean difference.
b. Test whether the population mean difference is zero (the null hypothesis) versus a two-tailed alternative. State whether you should accept or reject the null hypothesis, and why.
c. Repeat part b, but now restrict the population to stores where the competitor is not running a promotion of its own.
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?