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
A			B			C
	15			32			20
	13			32			26
	14			32			24
	19			35			26
	16			35			25

  

You will need to enter the data into Minitab. It is easiest to copy from here into Excel. Then copy and paste from Excel into Minitab. Besure that row 1 (the first white row in the spreadsheet) contains the first piece of data and that variable names are in the top grey row in Minitab.

  

(a)	Test the null hypothesis that μA, μB, and μC are equal by setting α = .05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

F
p-value

(Click to select)  Do not reject  Reject   H0: bottle design  (Click to select)  does not  does  have an impact on sales.

(b)	Based on Tukey's results, which bottle design maximizes mean daily sales?

Bottle design  (Click to select)  B  C  A   maximizes sales.

Answer 1

using minitab>Stat>ANOVA>one way ANOVA

we have

One-way ANOVA: A, B, C

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 A, B, C

Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Factor 2 792.13 93.31% 792.13 396.067 83.68 0.000
Error 12 56.80 6.69% 56.80 4.733
Total 14 848.93 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
2.17562 93.31% 92.19% 88.75 89.55%

Means

Factor N Mean StDev 95% CI
A 5 15.40 2.30 ( 13.28, 17.52)
B 5 33.200 1.643 (31.080, 35.320)
C 5 24.20 2.49 ( 22.08, 26.32)

Pooled StDev = 2.17562

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
B 5 33.200 A
C 5 24.20 B
A 5 15.40 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 17.80 1.38 ( 14.13, 21.47) 12.94 0.000
C - A 8.80 1.38 ( 5.13, 12.47) 6.40 0.000
C - B -9.00 1.38 (-12.67, -5.33) -6.54 0.000

Individual confidence level = 97.94%

a )

F	83.68
p-value	0.000

Reject   H0: bottle design have an impact on sales.

b )

Bottle design B maximizes sales.