A consumer preference study compares the effects of three different bottle desig
ID: 3228713 • Letter: A
Question
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. The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. (a) Test the null hypothesis that mu A, mu B, and mu C 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 answer to 2 decimal places.) (b) Consider the pairwise differences mu B - mu A, mu C - mu A, and mu C - mu B. 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.) The q-0.05 value to use for part b is 3.77 (c) Find a 95 percent confidence interval for each of the treatment means mu A, mu B, mu C. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)Explanation / Answer
Answer:
MINITAB output:
One-way ANOVA: A, B, C
Method
Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
Factor 3 A, B, C
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Factor 2 656.13 328.067 43.36 0.000
Error 12 90.80 7.567
Total 14 746.93
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.75076 87.84% 85.82% 81.01%
C).
Means
Factor N Mean StDev 95% CI
A 5 16.60 2.30 (13.92, 19.28)
B 5 32.80 3.03 (30.12, 35.48)
C 5 24.80 2.86 (22.12, 27.48)
Pooled StDev = 2.75076
Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Factor N Mean Grouping
B 5 32.80 A
C 5 24.80 B
A 5 16.60 C
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
b).
Difference Difference SE of Adjusted
of Levels of Means Difference 95% CI T-Value P-Value
B - A 16.20 1.74 ( 11.56, 20.84) 9.31 0.000
C - A 8.20 1.74 ( 3.56, 12.84) 4.71 0.001
C - B -8.00 1.74 (-12.64, -3.36) -4.60 0.002
Individual confidence level = 97.94%
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