Question

In: Statistics and Probability

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

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.

Bottle Design Study Data
A B C
18 31 28
13 31 25
14 29 22
13 29 26
15 29 20

  

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 73 14.6 4.3
Design B 5 149 29.8 1.2
Design C 5 121 24.2 10.2
ANOVA
Source of Variation SS df MS F P-Value F crit
Between Groups 590.9333 2 295.4667 56.46 3.23E-06 3.88529
Within Groups 62.8 12.0 5.2333
Total 653.7333 14

(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.)

Point estimate Confidence interval
?B?A: , [, ]
?C?A: , [, ]
?C?B: , [, ]

Bottle design (Click to select)BAC 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.)

Confidence interval
?A: [, ]
?B: [, ]
?C: [, ]

Solutions

Expert Solution

(b)

The point estaimtes are:

Critical value for , df=12 and k=3 is

So Tukey's HSD will be

So confidence intervals are:

For :

Since confidence interval does not contain zero so we can conclude that populaiton means differ.

For :

Since confidence interval does not contain zero so we can conclude that populaiton means differ.

For :

Since confidence interval does not contain zero so we can conclude that populaiton means differ.

(C)

For 95% confidence interval of individual means, degree of freedom of t is df=n-1=4.

The critical value of t for 95% confidence interval is 2.776.

Formula for confidence interval is

Following table shows the confidence intervals:

Mean SD Lower limit Upper limit
A 14.6 2.074 12.03 17.17
B 29.8 1.095 28.44 31.16
C 24.2 3.194 20.23 28.17

Related Solutions

A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 17...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 16...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 17...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 16...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 16...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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 given below. Let μA, μB, and μC represent the mean daily sales using...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 19...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 13...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 15...
A consumer preference study compares the effects of three different bottle designs (A, B, and C)...
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. Bottle Design Study Data A B C 16...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT