A consumer preference study compares the effects of three differentbottle designs (A, B, and C) on sales ofa popular fabric softener. A completely randomized design isemployed. Specifically, 15 supermarkets of equal sales potentialare selected, and 5 of these supermarkets are randomly assigned toeach bottle design. The number of bottles sold in 24 hours at eachsupermarket is recorded. The data obtained are displayed in thefollowing table.
| Bottle Design Study Data |
| A | B | C |
| 17 | | | 34 | | | 21 | |
| 16 | | | 30 | | | 21 | |
| 13 | | | 34 | | | 28 | |
| 13 | | | 30 | | | 26 | |
| 16 | | | 34 | | | 25 | |
|
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 | 75 | 15.0 | 3.5 |
| Design B | 5 | 162 | 32.4 | 4.8 |
| Design C | 5 | 121 | 24.2 | 9.7 |
|
| ANOVA | | | | | | |
| Source ofVariation | SS | df | MS | F | P-Value | F crit |
| BetweenGroups | 757.7333 | 2 | 378.8667 | 63.14 | 3.23E-06 | 3.88529 |
| WithinGroups | 72.0 | 12.0 | 6.0000 | | | |
| Total | 829.7333 | 14 | | | | |
|
(a) Test the null hypothesis that?A, ?B, and?C are equal by setting ? = .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.)
(Click to select)Do not rejectReject H0:bottle design (Click to select)doesdoes not have an impact onsales.
(b) Consider the pairwise differences?B – ?A,?C – ?A , and?C – ?B. 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 |
| ?B –?A: , [, ] |
| ?C –?A: , [, ] |
| ?C –?B: , [, ] |
|
Bottle design (Click to select)ACB maximizes sales.
(c) Find a 95 percent confidence interval foreach of the treatment means ?A,?B, and ?C. Interpret theseintervals. (Round your answers to 2 decimal places.Negative amounts should be indicated by a minus sign.)
| Confidenceinterval |
| ?A: [, ] |
| ?B: [, ] |
| ?C: [, ] |
|
