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 |
| 16 | | | 33 | | | 23 | |
| 18 | | | 31 | | | 27 | |
| 19 | | | 37 | | | 21 | |
| 17 | | | 29 | | | 28 | |
| 13 | | | 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 | 83 | 16.6 | 5.3 |
| Design B | 5 | 164 | 32.8 | 9.2 |
| Design C | 5 | 124 | 24.8 | 8.2 |
|
| ANOVA | | | | | | |
| Source of Variation | SS | df | MS | F | P-Value | F crit |
| Between Groups | 656.1333 | 2 | 328.0667 | 43.35683 | 3.23E-06 | 3.88529 |
| Within Groups | 90.8 | 12 | 7.566667 | | | |
| Total | 746.9333 | 14 | | | | |
|
  Click here for the Excel Data File
(a) Test the null hypothesis thatμA, μB,and μC are equal by setting α= .05. Based on this test, can we conclude that bottle designsA, B, and C have different effects onmean daily sales? (Round your answer to 2 decimalplaces.)
(b) Consider the pairwise differencesμB – μA,μC – μA ,and μC –μB. Find a point estimate of and aTukey simultaneous 95 percent confidence interval for each pairwisedifference. Interpret the results in practical terms. Which bottledesign maximizes mean daily sales? (Round your answers to 2decimal places. Negative amounts should be indicated by a minussign.)
(c) Find a 95 percent confidence interval foreach of the treatment means μA,μB, and μC. (Roundyour answers to 2 decimal places. Negative amounts should beindicated by a minus sign.)
