Several new methods of casting are being investigated in a foundry. There are fo
ID: 3333198 • Letter: S
Question
Several new methods of casting are being investigated in a foundry. There are four methods that will be compared. In the experiment, a heat (or melt) of metal is prepared and then used (in a random order) with each of the 4 methods. Prior experience suggests that the heats differ considerably so that it was important to have each of the treatments represented in each heat. Five heats were used. The data is summarized below:
Quality Assessment of Castings
Answer the following:
(a) Explain what the appropriate design is for this experiment and why.
(b) Provide an analysis of this design.
(c) Determine whether the quality differs among the casting methods. Use the 5% level of significance.
(e) If quality differs among methods, determine which method(s) provide the highes mean quality. Use the 5% level of significance.
Heat Method 1 2 3 4 5 A 49 52 67 86 66 B 55 52 82 78 68 C 46 57 62 78 60 D 72 67 86 98 72Explanation / Answer
Answer:
Several new methods of casting are being investigated in a foundry. There are four methods that will be compared. In the experiment, a heat (or melt) of metal is prepared and then used (in a random order) with each of the 4 methods. Prior experience suggests that the heats differ considerably so that it was important to have each of the treatments represented in each heat. Five heats were used. The data is summarized below:
Quality Assessment of Castings
Heat
Method
1
2
3
4
5
A
49
52
67
86
66
B
55
52
82
78
68
C
46
57
62
78
60
D
72
67
86
98
72
Answer the following:
Two factor design is used. The factors are method and heat. Method is 4 levels and heat is with 5 levels.
(b) Provide an analysis of this design.
Randomized blocks ANOVA
Mean
n
Std. Dev
64.000
5
14.714
A
67.000
5
13.379
B
60.600
5
11.524
C
79.000
5
12.767
D
55.500
4
11.619
H1
57.000
4
7.071
H2
74.250
4
11.558
H3
85.000
4
9.452
H4
66.500
4
5.000
H5
67.650
20
14.005
Total
ANOVA table
Source
SS
df
MS
F
p-value
Treatments
961.35
3
320.450
11.40
0.0008
Blocks
2,427.80
4
606.950
21.59
0.0000
Error
337.40
12
28.117
Total
3,726.55
19
Post hoc analysis
p-values for pairwise t-tests
C
A
B
D
60.600
64.000
67.000
79.000
C
60.600
A
64.000
.3307
B
67.000
.0805
.3886
D
79.000
.0001
.0008
.0038
Tukey simultaneous comparison t-values (d.f. = 12)
C
A
B
D
60.600
64.000
67.000
79.000
C
60.600
A
64.000
1.01
B
67.000
1.91
0.89
D
79.000
5.49
4.47
3.58
(c) Determine whether the quality differs among the casting methods. Use the 5% level of significance.
Calculated F=11.40, P=0.0008 which is < 0.05 level. Ho is rejected.
There is significant difference among the casting methods.
(e) If quality differs among methods, determine which method(s) provide the highes mean quality. Use the 5% level of significance.
Quality D differ significantly high among the 4 methods.
Heat
Method
1
2
3
4
5
A
49
52
67
86
66
B
55
52
82
78
68
C
46
57
62
78
60
D
72
67
86
98
72
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