A consumer preference study compares the effects of three different bottle desig
ID: 3365550 • Letter: A
Question
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)doesdoes not 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)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.)
Bottle Design Study Data A B C 17 29 23 18 30 24 17 33 22 14 33 23 17 31 21Explanation / Answer
Result:
MINITAB used.
(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.)
F
118.79
p-value
0.000
(Click to select)Reject: bottle design (Click to select)does 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.)
Point estimate Confidence interval
B –A: , [, ]
C –A: , [, ]
C –B: , [, ]
Difference
of Levels
Difference
of Means
SE of
Difference
95% CI
B - A
14.600
0.952
(12.06, 17.14)
C - A
6.000
0.952
(3.46, 8.54)
C - B
-8.600
0.952
(-11.14, -6.06)
We are 95% confidence that mean sales difference of all B-A types falls in the interval (12.06, 17.14).
We are 95% confidence that mean sales difference of all C-A types falls in the interval (3.46, 8.54)
We are 95% confidence that mean sales difference of all C-B types falls in the interval (-11.14, -6.06).
Bottle design B 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
Factor
N
Mean
StDev
95% CI
A
5
16.600
1.517
(15.13, 18.07)
B
5
31.200
1.789
(29.73, 32.67)
C
5
22.600
1.140
(21.13, 24.07)
We are 95% confident the mean sales of all bottle of type A falls in the interval (15.13, 18.07).
We are 95% confident the mean sales of all bottle of type B falls in the interval (29.73, 32.67).
We are 95% confident the mean sales of all bottle of type C falls in the interval (21.13, 24.07).
One-way ANOVA: A, B, C
Method
Null hypothesis
All means are equal
Alternative hypothesis
Not all means are equal
Significance level
= 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor
Levels
Values
Factor
3
A, B, C
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Factor
2
538.53
269.267
118.79
0.000
Error
12
27.20
2.267
Total
14
565.73
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
1.50555
95.19%
94.39%
92.49%
Means
Factor
N
Mean
StDev
95% CI
A
5
16.600
1.517
(15.133, 18.067)
B
5
31.200
1.789
(29.733, 32.667)
C
5
22.600
1.140
(21.133, 24.067)
Pooled StDev = 1.50555
Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Factor
N
Mean
Grouping
B
5
31.200
A
C
5
22.600
B
A
5
16.600
C
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference
of Levels
Difference
of Means
SE of
Difference
95% CI
T-Value
Adjusted
P-Value
B - A
14.600
0.952
(12.062, 17.138)
15.33
0.000
C - A
6.000
0.952
(3.462, 8.538)
6.30
0.000
C - B
-8.600
0.952
(-11.138, -6.062)
-9.03
0.000
Individual confidence level = 97.94%
F
118.79
p-value
0.000
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