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The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment

Statistics Oct 29, 2020

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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