An industrial engineer employed by a beverage bottler is interested in potential
ID: 3349849 • Letter: A
Question
An industrial engineer employed by a beverage bottler is interested in potential fatigue differences resulting from the effects of two different types of 32-ounce bottles on the time to deliver 12-bottle cases of the product. The two bottle types are glass and plastic. As a measure of the amount of effort required, he measured the elevation of the heart rate (pulse) induced by the task. Four replicates of a 22 factorial design are performed, the results follow. Analyze the data and draw conclusions. Worker Bottle Type 39 58 45 35 35 21 20 16 13 16 Glass 13 Plastic 10 42 15Explanation / Answer
Result:
bottle type
worker1
worker 2
Total
Total glass
Glass
39
20
59
45
13
58
58
16
74
35
11
46
237
plastic
44
13
57
35
10
45
42
16
58
21
15
36
196
Total
319
114
433
Squares of all numbers
Total
1521
400
1921
2025
169
2194
3364
256
3620
1225
121
1346
1936
169
2105
1225
100
1325
1764
256
2020
441
225
666
Total
13501
1696
15197
Correction factor CF = 433^2/16 =11718.1
Total sum of squares = 39^2+45^2+…… -433^2/16
=15197-433^2/16 =3478.94
SS worker = 319^2/8+114^2/8 -433^2/16 =2626.56
SS glass = 237^2/8+196^2/8 -433^2/16 = 105.06
SS interaction = 177^2/4+60^2/4+142^2/4+54^2/4 -433^2/16 -2626.56-105.06 =52.56
Two factor ANOVA
Factor 2
Means:
Worker1
Worker2
Glass
44.3
15.0
29.6
Factor 1
Plastic
35.5
13.5
24.5
39.9
14.3
27.1
4
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 Bottle type
105.06
1
105.063
1.81
.2028
Factor 2 worker
2,626.56
1
2,626.563
45.37
0.0000
Interaction
52.56
1
52.563
0.91
.3595
Error
694.75
12
57.896
Total
3,478.94
15
To test the bottle type effect, calculated F=1.81, P=0.2028 which is > 0.05 level of significance. The effect of bottle type is not significant.
To test the worker effect, calculated F=45.37, P=0.0000 which is < 0.05 level of significance. The effect of worker is significant.
To test the interaction effect, calculated F=0.91, P=0.3595 which is > 0.05 level of significance. The effect of interaction is not significant.
bottle type
worker1
worker 2
Total
Total glass
Glass
39
20
59
45
13
58
58
16
74
35
11
46
237
plastic
44
13
57
35
10
45
42
16
58
21
15
36
196
Total
319
114
433