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 the following table. Bottle Design Study Data A B C 13 29 28 16 35 27 16 31 22 14 29 26 14 31 26 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. SUMMARY Groups Count Sum Average Variance Design A 5 73 14.6 1.8 Design B 5 155 31.0 6.0 Design C 5 129 25.8 5.2 ANOVA Source of Variation Between Groups Within Groups Total SS 702.4000 52.0 754.4000 df 2 12.0 14 MS 351.2000 4.3330 F 81.05 P-Value 1.07E-07 F crit 3.88529 (a) Test the null hypothesis that A, MB, and c are equal by setting a = .05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places.) F = p-value = Reject 0.000 HO: bottle design 68.65 x does have an impact on sales. (b) Consider the pairwise differences B - MA, MC - M, and C - MB. 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? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Point estimate Confidence interval B -A: C-A: | UC UB: 16.20 >, [ 6.60 .[ (9.60), [ 12.49 19.91 2.89 X (13.31) X 10.31 x 1 (5.89)] Bottle design B maximizes sales. (c) Find a 95 percent confidence interval for each of the treatment means , MB, and c. Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Confidence interval A: [ 14.27 x UB: [ 30.47 x C: [ 23.77 19.73 x 33.03 27.83