Consider a large chain of supermarkets that sells its own brand of potato chips in addition to many other name brands. Management would like to know whether the type of display used for the store brand has any effect on sales. Because there are four types of displays being considered, management decides to choose 24 similar stores to serve as experimental units.
A random six of these are instructed to use display type 1, another random six are instructed to use display type 2, a third random six are instructed to use display type 3, and the final six stores are instructed to use display type 4. For a period of one month, each store keeps track of the fraction of total potato chips sales that are of the store brand. The data for the 24 stores are shown in the file P09_54.xlsx. Note that one of the stores using display 3 has a blank cell. This store did not follow instructions properly, so its observation is disregarded.
a. Why do you think each store keeps track of the fraction of total potato chips sales that are of the store brand? Why do they not simply record the total amount of sales of the store brand potato chips?
b. Do the data suggest different mean proportions of store brand sales at the 10% significance level? If so, use 90% confidence intervals for the differences between all pairs of mean proportions to identify which of the display types are associated with higher fractions of sales.