Reference no: EM132465031
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 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.
SUMMARYGroupsCountSumAverageVarianceDesign A58116.25.7Design B515731.41.8Design C512424.87.7
ANOVA Source of VariationSSdfMSFP-ValueF critBetween Groups580.93332290.466757.337.23E-073.88529Within Groups60.812.05.0670 Total641.733314
(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 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? (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, andμC. Interpret these intervals.(Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
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