A research team wished to specify a manufacturing process so that Y, the area in
ID: 3251520 • Letter: A
Question
A research team wished to specify a manufacturing process so that Y, the area in a product affected by surface flaws was as small as possible. They had four levels of concentration of a chemical used to wash the product before the final manufacturing step and wanted to determine whether different concentration levels caused a change in E(Y). They ran a balanced one-way layout with 6 observations at each concentration with level 1 set at 5%, level 2 set at 10%, level 3 set at 15%, and level 4 set at 20%. They observed that y, =21.5, y_2 = 11.2, y_3 = 18.8, and y_4 = 39.3, where y_i. was the average of the observations taken on the ith level. They also observed that s_1^2 = 81.9, s_2^2 = 92.2, s_3^2 = 71.8, and s_4^2 = 101.9, where s_1^2 was the unbiased estimate of the variance for the observations taken at the ith concentraton. The four parts of this problem are worth a total of 80 points. a. Complete the analysis of variance table for these results; that is, be sure to specify the degrees of freedom, sum of squares, mean square, and F-test. Use significance levels set to 0.10, 0.05, and 0.01.Explanation / Answer
Answer:
Group
Mean
SD
n
Total
SSGroups
SSError
1
21.5
9.049862
6
129
8.64
409.5
2
11.2
9.602083
6
67.2
793.5
461
3
18.8
8.473488
6
112.8
91.26
359
4
39.3
10.09455
6
235.8
1653.36
509.5
ANOVA
Source
df
SS
MS
F
P-value
Groups
3
2546.76
848.92
9.763312
0.000356
Error
20
1739
86.95
Total
23
4285.76
H_0: mu_1 = mu_2= mu_3 = mu_4
H1: At least one pair of population means are different
Calculated F=9.76, P=0.0004 which is < 0.01 level.
Ho is rejected at all the 0.10, 0.05 and 0.01 levels.
Group
Mean
SD
n
Total
SSGroups
SSError
1
21.5
9.049862
6
129
8.64
409.5
2
11.2
9.602083
6
67.2
793.5
461
3
18.8
8.473488
6
112.8
91.26
359
4
39.3
10.09455
6
235.8
1653.36
509.5
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