A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in Table 11.5. Let μA, μB, and μC represent mean daily sales using bottle designs A, B, and C, respectively. Figure 11.5 gives the Excel output of a one- way ANOVA of the bottle design study data. Using the computer output:
a. Test the null hypothesis that are equal by setting α = .05. That is, test for statistically significant differences between these treatment means at the .05 level of significance. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales?
b. Consider the pairwise differences μB – μA, μC – μA, and μC – μB. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales?
c. Find and interpret a 95 percent confidence interval for each of the treatment means μA, μB, and μC.