A consumer preference study compares the effects of three different bottle designs (A,B, andC) 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

17 29 23

18 30 24

17 33 22

14 33 23

17 31 21

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

SUMMARY

Groups Count Sum Average Variance

Design A 5 83 16.6 2.3

Design B 5 156 31.2 3.2

Design C 5 113 22.6 1.3

ANOVA

Source of Variation SS df MS F P-Value F crit

Between Groups 538.5333 2 269.2667 118.79 1.24E-08 3.88529

Within Groups 27.2 12.0 2.2670

Total 565.7333 14

(a)Test the null hypothesis that_A,_B, and_Care 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.)

F =

p-value =

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.)

uB - uA

uC - uA

uC - uB

(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

uA: [ _______ , ______]

uB: [ _______ , ______]

uC: [ _______, _______]