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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

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 VariationSSdfMSF

**(a)** Test the null hypothesis that *μ _{A}*,

**(b)** Consider the pairwise differences *μ _{B}* –

**(c)** Find a 95 percent confidence interval for each of the treatment means *μ _{A}*,

(a) To test the null hypothesis that μA, μB, and μC are equal, we can use the one-way ANOVA test.

The...