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[answered] A consumer preference study compares the effects of three d


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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

 

19

 

34

 

26

 

18

 

33

 

24

 

14

 

35

 

23

 

17

 

30

 

21

 

14

 

31

 

27 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

 

SUMMARY

 

Coun

 

Groups

 

Sum AverageVariance

 

t

 

Design A 5

 

82

 

16.4

 

5.3

 

Design B 5 163

 

32.6

 

4.3

 

Design C 5 121

 

24.2

 

5.7 ANOVA

 

Source of Variation SS df MS Between Groups 656.4000 2 328.2000 Within Groups

 

Total 61.2 12.0

 

717.6000

 

14 5.1000 F P-Value F crit

 

3.23E64.35

 

3.88529

 

06 (a) Test the null hypothesis that ?A, ?B, and ?C are equal by setting ? = .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

 

pvalue H0: bottle design

 

(Click to select) have an impact on sales.

 

(Click to select) (b) Consider the pairwise differences ?B ? ?A, ?C ? ?A , and ?C ? ?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.)

 

Point estimate Confidence interval

 

?B ??A:

 

,[

 

, ?C ??A: ,[ , ?C ??B: ,[ , Bottle design maximizes sales.

 

(Click to select) (c) Find a 95 percent confidence interval for each of the treatment means ?A, ?B, and ?C. Interpret

 

these intervals. (Round your answers to 2 decimal places. Negative amounts should be

 

indicated by a minus sign.)

 

Confidence interval

 

?A: [

 

, ?B: [ , ? C: [ ,

 


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