11.47 Demand for Diamonds A chain of jewellery stores conducted an experiment to investigate the effect of price and location on the demand for its diamonds. Six small-town stores were selected for the study, as well as six stores located in large suburban malls. Two stores in each of these locations were assigned to each of three item percentage markups. The percentage gain (or loss) in sales for each store was recorded at the end of 1 month. The data are shown in the accompanying table.

a. Do the data provide sufficient evidence to indicate an interaction between markup and location? Test using a = 0.05.

b. What are the practical implications of your test in part a?

c. Draw a line graph similar to Figure 11.9 to help visualize the results of this experiment. Summarize the results.

d. Find a 95% confidence interval for the difference in mean change in sales for stores in small towns versus those in suburban malls if the stores are using price markup 3.

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Markup Location 1 2 3 Small towns 10 -3 -10 4 7 -24 Suburban malls 14 18 83 8 3 3