Robert Altoff is vice president for engineering for a manufacturer of household
ID: 3292744 • Letter: R
Question
Robert Altoff is vice president for engineering for a manufacturer of household washing machines. As part of new product development, he wishes to determine the optimal length of time for the washing cycle. A part of the development is to study the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown below.
Complete an ANOVA table. Use the .05 significance level. (Round SS, MS, p to 3 decimal places and F to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)
(Click to select)A.)Both the cycle time mean and the brand mean are significantly different B.)Only the cycle time means are significantly different C.)Both the cycle time mean and the brand mean are not significantly different D.)Only the brand means are significantly different from the values calculated.
Cycle Time (min) Detergent Brand 18 20 22 24 A .21 .15 .23 .16 .11 .11 .17 .18 B .14 .15 .18 .20 .10 .14 .17 .18 C .16 .15 .18 .19 .17 .14 .19 .21 D .09 .12 .16 .15 .13 .13 .16 .17Explanation / Answer
Answer:
Complete an ANOVA table. Use the .05 significance level. (Round SS, MS, p to 3 decimal places and F to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)
ANOVA table
Source
SS
df
MS
F
p-value
Cycle
0.014
3
0.005
7.50
.0024
Brand
0.005
3
0.002
2.76
.0764
Interaction
0.004
9
0.000
0.63
.7560
Error
0.010
16
0.001
Total
0.034
31
b-1.
Find the cycle mean values. (Round your answers to 3 decimal places.)
Cycle
Mean
18 Min
0.139
20 Min
0.136
22 Min
0.180
24 Min
0.180
b-2.
Find the brand mean values. (Round your answers to 3 decimal places.)
Brand
Mean
A
0.165
B
0.158
C
0.174
D
0.139
A.)Both the cycle time mean and the brand mean are significantly different
Answer: B.)Only the cycle time means are significantly different
C.)Both the cycle time mean and the brand mean are not significantly different
D.)Only the brand means are significantly different from the values calculated.
Two factor ANOVA
Factor 2
Means:
time18
time20
time22
time24
A
0.160
0.130
0.200
0.170
0.165
Factor 1
B
0.120
0.145
0.175
0.190
0.158
C
0.165
0.145
0.185
0.200
0.174
D
0.110
0.125
0.160
0.160
0.139
0.139
0.136
0.180
0.180
0.159
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Cycle
0.0145
3
0.00483
7.50
.0024
Brand
0.0053
3
0.00178
2.76
.0764
Interaction
0.0036
9
0.00041
0.63
.7560
Error
0.0103
16
0.00064
Total
0.0338
31
ANOVA table
Source
SS
df
MS
F
p-value
Cycle
0.014
3
0.005
7.50
.0024
Brand
0.005
3
0.002
2.76
.0764
Interaction
0.004
9
0.000
0.63
.7560
Error
0.010
16
0.001
Total
0.034
31
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