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 |
| 19 | | | 30 | | | 25 | |
| 17 | | | 30 | | | 20 | |
| 18 | | | 33 | | | 22 | |
| 15 | | | 35 | | | 27 | |
| 18 | | | 29 | | | 21 | |
|
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 | 87 | 17.4 | 2.3 |
| Design B | 5 | 157 | 31.4 | 6.3 |
| Design C | 5 | 115 | 23.0 | 8.5 |
|
| ANOVA | | | | | | |
| Source of Variation | SS | df | MS | F | P-Value | F crit |
| Between Groups | 496.5333 | 2 | 248.2667 | 43.56 | 3.23E-06 | 3.88529 |
| Within Groups | 68.4 | 12.0 | 5.7000 | | | |
| Total | 564.9333 | 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.)
(Click to select)Do not rejectReject H0:bottle design (Click to select)doesdoes 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 estimate Confidence interval |
| μB –μA: , [, ] |
| μC –μA: , [, ] |
| μC –μB: , [, ] |
|
Bottle design (Click to select)CBA 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.)
| Confidence interval |
| μA: [, ] |
| μB: [, ] |
| μC: [, ] |
