3.00 points A consumer preference study compares the efects of three cifferent b
ID: 2946855 • Letter: 3
Question
3.00 points A consumer preference study compares the efects of three cifferent bottle des gns (A, B, and C) on salas of a popu ar fabric softener. A complately randomized design is employed. Specifically. 15 supermarkets of equal sales potenal are selected, and 5 of these super markets are randomly assigned to each bottle desagn. The number o battles sold n 24 hours at each supermarkt ts recorded. The data cbta ned are displayed n the fol owing table Bowe Design Study Data 34 16 04 25 The Excel output of a one-way ANOVA of the Bottie Design Study Data is shown below. Count Sum Average Variance Design A Design B Desion C 86 163 128 32.6 256 28 6.3 Source of Variation Between Groupe Wthin Groups PValue 3.23E-06 3.8 F crt 5945333 297.2667 91.00 633 7333 a Test the null hypothesis that enter "O" wherever required.) A B and K are equal by setting ?= 05 Based on this test can we conclude hat bottie designs A and Chave ditie ent effects on mean daly sales? Round your answers to 2 deci al places. Leave no cells blank be certain to 43.36Explanation / Answer
Result:
a).
F=91.00
P=0.00
b).
Difference
of Levels
Difference
of Means
SE of
Difference
95% CI
T-Value
Adjusted
P-Value
B - A
15.40
1.14
(12.35, 18.45)
13.47
0.000
C - A
8.40
1.14
(5.35, 11.45)
7.35
0.000
C - B
-7.00
1.14
(-10.05, -3.95)
-6.12
0.000
c).
Factor
N
Mean
StDev
95% CI
A
5
17.200
0.837
(15.44, 18.96)
B
5
32.600
1.673
(30.84, 34.36)
C
5
25.60
2.51
(23.84, 27.36)
MINITAB used.
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
594.53
297.267
91.00
0.000
Error
12
39.20
3.267
Total
14
633.73
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
1.80739
93.81%
92.78%
90.34%
Means
Factor
N
Mean
StDev
95% CI
A
5
17.200
0.837
(15.439, 18.961)
B
5
32.600
1.673
(30.839, 34.361)
C
5
25.60
2.51
(23.84, 27.36)
Pooled StDev = 1.80739
Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Factor
N
Mean
Grouping
B
5
32.600
A
C
5
25.60
B
A
5
17.200
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
15.40
1.14
(12.35, 18.45)
13.47
0.000
C - A
8.40
1.14
(5.35, 11.45)
7.35
0.000
C - B
-7.00
1.14
(-10.05, -3.95)
-6.12
0.000
Individual confidence level = 97.94%
Difference
of Levels
Difference
of Means
SE of
Difference
95% CI
T-Value
Adjusted
P-Value
B - A
15.40
1.14
(12.35, 18.45)
13.47
0.000
C - A
8.40
1.14
(5.35, 11.45)
7.35
0.000
C - B
-7.00
1.14
(-10.05, -3.95)
-6.12
0.000
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