Exercise 11.7 METHODS AND APPLICATIONS A consumer preference study compares the

Question

Exercise 11.7 METHODS AND APPLICATIONS

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

  

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

(a) Test the null hypothesis that A, B, and C are 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. Leave no cells blank - be certain to enter "0" wherever required.)

(Click to select)RejectDo not reject H0: bottle design (Click to select)does notdoes have an impact on sales.

(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.)

Bottle design (Click to select)BCA maximizes sales.

(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.)

Bottle Design Study Data A B C 17 29 23 18 30 24 17 33 22 14 33 23 17 31 21

Explanation / Answer

we are given the one way ANOVA,

consider the table a)

Test the null hypothesis that A, B, and C are 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?

if p< 0.05 then we reject the null hypothesis and conclude that there is significant diffreance between the goups.

here p<0.05 , so we can colcude that there is significant diffreance between the three bottle designs.

the out put of tukey test is,

so here all p-value are are significant, so there are all significant diffreances significant

to find the confidance interval, we have to udse the one sample test, and in sample t-test we can comaire the diffreance between the observed mean and hypothised mean.

here hypothized values are not provided, please prove hypothies value for ferther calculation.

Thanks

F p-value 3.23E-06

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