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# (Solved): A consumer preference study compares the effects of three different bottle designs (A, B, and C) on ...

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 DataABC 14 31 24 17 32 25 13 29 28 14 30 27 15 34 28

The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

SUMMARYGroupsCountSumAverageVarianceDesign A57314.62.3Design B515631.23.7Design C513226.43.3

ANOVA Source of VariationSSdfMSFP-ValueF critBetween Groups729.73332364.8667117.701.30E-083.88529Within Groups37.212.03.1000 Total766.933314

(a) Test the null hypothesis that μA, μB, and μC are equal by setting α = .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.)

(b) Consider the pairwise differences μBμA, μCμA , and μCμB. 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.)

(c) Find a 95 percent confidence interval for each of the treatment means μA, μB, and μC. Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

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