Robert Altoff is vice president for engineering for a manufacturer of household
ID: 3265714 • 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. Cycle Time (min) Detergent Brand 18 20 22 24 A .12 .12 .21 .19 .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 .17 a. 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.) Source df SS MS F p Cycle Brand Interaction Error Total b-1. Find the cycle mean values. (Round your answers to 3 decimal places.) Cycle Mean 18 Min 20 Min 22 Min 24 Min b-2. Find the brand mean values. (Round your answers to 3 decimal places.) Brand Mean A B C D d. Choose the right option a. For the p-value calculated there is . b. from the values calculated. c. The confidence interval indicate that cycle times of 22 and 24 minutes are to alternatives.
Explanation / Answer
(a)
Source
DF
SS
MS
F
P
Cycle
3
0.005
0.002
7.86
0.002
Brand
3
0.021
0.007
32.09
-0.000
Interaction
9
0.003
0.000
1.20
0.231
Error
16
0.003
0.000
Total
31
0.032
(b-1)
Cycle
Mean
18 Min
0.128
20 Min
0.133
22 Min
0.178
24Min0.184
(b-2)
Brand
Mean
A
0151
B
0.158
C
0.174
D
Answer:
Two factor ANOVA
Factor 2
Means:
18
20
22
24
A
0.115
0.115
0.190
0.185
0.151
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
0.128
0.133
0.178
0.184
0.155
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1
0.005
3
0.002
7.86
0.002
Factor 2
0.021
3
0.007
32.09
0.000
Interaction
0.003
9
0.000
1.50
0.231
Error
0.003
16
0.000
Total
0.032
31
(a)
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