Exercise 12.7 (Algo) METHODS AND APPLICATIONS 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 15 32 26 13 30 28 18 33 21 16 30 23 19 32 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 81 16.2 5.7 Design B 5 157 31.4 1.3 Design C 5 124 24.8 7.7 ANOVA Source of Variation SS df MS F P-Value F crit Between Groups 580.9333 2 290 . 4667 57.33 7. 23E-07 3. 88529 Within Groups 60.8 12.0 5 . 0670 Total 641 . 7333 14 (a) Test the null hypothesis that MA, MB, and uc 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.) Answer is complete and correct. F = 57.33 p-value = 0.000 Reject HO: bottle design does have an impact on sales.(b) Consider the pairwise differences us - MA, UC - MA, and uc - 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.) x Answer is complete but not entirely correct. Point estimate Confidence interval MB -UA: 0. 12 X 0.45 X 0.04 X UC -UA: 0.32 X 0.82 X 0.34 X UC -UB: 0.44 X 0.48 X 1.34 X(c) Find a 95 percent confidence interval for each of the treatment means \"A, p3, and #c- Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Q Answer is complete but not entirely correct. Condence interval