Question

In: Statistics and Probability

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

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 34 26
17 31 23
13 34 28
14 32 27
16 30 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 3.3
Design B 5 161 32.2 3.2
Design C 5 130 26.0 3.5
ANOVA
Source of Variation SS df MS F P-Value F crit
Between Groups 796.9333 2 398.4667 119.54 3.23E-06 3.88529
Within Groups 40.0 12.0 3.3333
Total 836.9333 14

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.)

Confidence interval
μA: [  ,  ]
μB: [  ,  ]
μC: [  ,  ]

Solutions

Expert Solution

Answer: 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.

Solution:


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