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 17 16 18 19 31 35 35 31 25 20 27 26 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below SUMMARY Groups Design A Design B Design C Count Sum Average Variance 83 165 120 16.6 33.0 24.0 5.3 4.0 8.5 ANOVA Source of Variation Between Groups Within Groups Total P.Value 3.23E-06 F crit 3.88529 df MS 674.5333 337.2667 56.84 71.2 12.0 5.9333 745.7333

Explanation / Answer

Answer

Here ;

USING MINITAB

Results are as follows

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 95%CI   

of Levels     of Means   

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.

Here is the Factor Information :-

Factor Levels Values

Factor       3 A, B, C

The Analysis of Variance is shown below:-

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% Confidence Interval

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 Standard Deviation = 2.43584

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence Level are as :-

Factor N    Mean Grouping

B 5 33.000 A

C 5 24.00 B

A 5 16.60 C

Means which don't 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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