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The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment
The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment.
|
Source |
DF |
SS |
MS |
F |
P |
|
A |
1 |
0.322 |
- |
- |
- |
|
B |
- |
80.554 |
40.2771 |
4.59 |
- |
|
Interaction |
- |
- |
- |
- |
- |
|
Error |
12 |
105.327 |
8.7773 |
- |
- |
|
Total |
17 |
231.551 |
|
|
|
(a) Fill in the blanks in the ANOVA table. You can use bounds on the P-values.
(b) How many levels were used for factor B?
(c) How many replicates of the experiment were per-formed?
(d) What conclusions would you draw about this experiment?
5.6. An article in Industrial Quality Canby! (1956, pp. 5-8) describes an experiment to investigate the effect of the type of glass and the type of phosphor on the brightness of a television tube. The response variable is the current necessary (in microamps) to obtain a specified brightness level. The data are as follows:
|
Glass Type
|
Phosphor Type |
||
|
1 |
2 |
3 |
|
|
1 |
280 |
300 |
290 |
|
290 |
310 |
285 |
|
|
285 |
295 |
290 |
|
|
2 |
230 |
260 |
220 |
|
235 |
240 |
225 |
|
|
240 |
235 |
230 |
|
(a) Is there any indication that either factor influences brightness? Use a = 0.05.
(b) Do the two factors interact? Use a = 0.05.
(c) Analyze the residuals from this experiment.
5.8. The factors that influence the breaking strength of a synthetic fiber are being studied. Four production machines and three operators are chosen and a factorial experiment is run using fiber from the same production batch. The results are as follows:
|
Operator
|
Machine |
|
||
|
1 |
2 |
3 |
4 |
|
|
1 |
109 |
110 |
108 |
110 |
|
110 |
115 |
109 |
108 |
|
|
110 |
110 |
111 |
114 |
|
|
2 |
112 |
111 |
109 |
112 |
|
116 |
112 |
114 |
120 |
|
|
114 |
115 |
119 |
117 |
|
(a) Analyze the data and draw conclusions. Use a = 0.05.
(b) Prepare appropriate residual plots and comment on the model's adequacy.
5.23 Consider the data in problem 5.8 Analyze the data. Assuming that replicates are blocks.
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