A consumer preference study compares the effects of threedifferent bottle designs (A, B, and C)on sales of a popular fabric softener. A completely randomizeddesign is employed. Specifically, 15 supermarkets of equal salespotential are selected, and 5 of these supermarkets are randomlyassigned to each bottle design. The number of bottles sold in 24hours at each supermarket is recorded. The data obtained aredisplayed in the following table.
| Bottle Design Study Data |
| A | B | C |
| 13 | | | 29 | | | 28 | |
| 16 | | | 35 | | | 27 | |
| 16 | | | 31 | | | 22 | |
| 14 | | | 29 | | | 26 | |
| 14 | | | 31 | | | 26 | |
|
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The Excel output of a one-way ANOVA of the Bottle Design StudyData is shown below.
| SUMMARY |
| Groups | Count | Sum | Average | Variance |
| Design A | 5 | 73 | 14.6 | 1.8 |
| Design B | 5 | 155 | 31.0 | 6.0 |
| Design C | 5 | 129 | 25.8 | 5.2 |
|
| ANOVA | | | | | | |
| Source ofVariation | SS | df | MS | F | P-Value | F crit |
| BetweenGroups | 702.4000 | 2 | 351.2000 | 81.05 | 3.23E-06 | 3.88529 |
| WithinGroups | 52.0 | 12.0 | 4.3333 | | | |
| Total | 754.4000 | 14 | | | | |
|
(a) Test the null hypothesis thatμA, μB, andμC are equal by setting α = .05. Basedon this test, can we conclude that bottle designs A, B, and C havedifferent effects on mean daily sales? (Round your answersto 2 decimal places. Leave no cells blank - becertain to enter \"0\" whereverrequired.)
| |
F-statistic ( Â Â ) | |
| p-value ( Â Â ) | |
|
(Click to select)Do not reject/Reject H0:bottle design (Click to select)does/does not have an impact onsales.
(b) Consider the pairwise differencesμB – μA,μC – μA , andμC – μB. Find a pointestimate of and a Tukey simultaneous 95 percent confidence intervalfor each pairwise difference. Interpret the results in practicalterms. Which bottle design maximizes mean daily sales?(Round your answers to 2 decimal places.Negative amounts should be indicated by a minussign.)
| Point estimateConfidence interval |
| μB –μA:   , [ ,  ] |
| μC –μA:   , [ ,  ] |
| μC –μB:   , [ ,  ] |
|
Bottle design (Click to select)B/C/A maximizes sales.
(c) Find a 95 percent confidence interval foreach of the treatment means μA,μB, and μC. Interpret theseintervals. (Round your answers to 2 decimal places.Negative amounts should be indicated by a minus sign.)
| Confidenceinterval |
| μA: [ ,   ] |
| μB: [ ,   ] |
| μC: [ ,   ] |
