A consumer preference study compares the effects of three different bottle desig

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. Bottle Design Study Data 25 20 27 26 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. SUMMARY Groups Count S Average Variance 16.6 Design A 83 5.3 Design B 165 33.0 4.0 8.5 Design C 5 20 24.0 ANOVA Source of Variation SS MS P-Value F crit 337.2667 56.84 3.23E-06 3.88529 Between Groups 674.5333 Within Groups 5.9333 2.0 745.7333 14 Total

Explanation / Answer

Answer:

MINITAB used.

F=56.84

P=0.000

Reject Ho. Bottle designs does have an impact on sales.

95% CI for mean difference Tukey Simultaneous Tests for Differences of Means

Difference Difference      

                          

of Levels     of Means

                           95% CI     

B - A            16.40        ( 12.29, 20.51)   

C - A             7.40        ( 3.29, 11.51)    

C - B            -9.00        (-13.11, -4.89)   

Means

Factor        95% CI

A        ( 14.23, 18.97)

B        (30.627, 35.373)

C        ( 21.63, 26.37)

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   2 674.53 337.267    56.84    0.000

Error   12   71.20    5.933

Total   14 745.73

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)

2.43584 90.45%     88.86%      85.08%

Means

Factor N    Mean StDev       95% CI

A       5   16.60   2.30 ( 14.23, 18.97)

B       5 33.000 2.000 (30.627, 35.373)

C       5   24.00   2.92 ( 21.63, 26.37)

Pooled StDev = 2.43584

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N    Mean Grouping

B       5 33.000 A

C       5   24.00    B

A       5   16.60      C

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference Difference       SE of                            Adjusted

of Levels     of Means Difference       95% CI      T-Value   P-Value

B - A            16.40        1.54 ( 12.29, 20.51)    10.65     0.000

C - A             7.40        1.54 ( 3.29, 11.51)     4.80     0.001

C - B            -9.00        1.54 (-13.11, -4.89)    -5.84     0.000

Individual confidence level = 97.94%

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