Assignment_Solution_Chp_5

Assignment_Solution_Chp_5 - Chapter 5 Solutions 5.2 The...

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Chapter 5– Solutions 5.2. The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment. Two-way ANOVA: y versus A, B Source DF SS MS F P A 1 ? 0.0002 ? ? B ? 180.378 ? ? ? Interaction 3 8.479 ? ? 0.932 Error 8 158.797 ? Total 15 347.653 (a) Fill in the blanks in the ANOVA table. You can use bounds on the P -values. Two-way ANOVA: y versus A, B Source DF SS MS F P A 1 0.0002 0.0002 0.00001 0.998 B 3 180.378 60.1260 3.02907 0.093 Interaction 3 8.479 2.8263 0.14239 0.932 Error 8 158.797 19.8496 Total 15 347.653 (a) How many levels were used for factor B ? 4 levels. (b) How many replicates of the experiment were performed? 2 replicates. (c) What conclusions would you draw about this experiment? Factor B is moderately significant with a P -value of 0.93. Factor A and the two-factor interaction are not significant. 5.7. Johnson and Leone ( Statistics and Experimental Design in Engineering and the Physical Sciences , Wiley 1977) describe an experiment to investigate the warping of copper plates. The two factors studied were the temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data were as follows: Copper Content (%) Temperature (°C) 40 60 80 100 50 17,20 16,21 24,22 28,27 75 12,9 18,13 17,12 27,31 100 16,12 18,21 25,23 30,23
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125 21,17 23,21 23,22 29,31 (a) Is there any indication that either factor affects the amount of warping? Is there any interaction between the factors? Use α = 0.05. Both factors, copper content ( A ) and temperature ( B ) affect warping, the interaction does not. Design Expert Output Response: Warping ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 968.22 15 64.55 9.52 < 0.0001 significant A 698.34 3 232.78 34.33 < 0.0001 B 156.09 3 52.03 7.67 0.0021 AB 113.78 9 12.64 1.86 0.1327 Residual 108.50 16 6.78 Lack of Fit 0.000 0 Pure Error 108.50 16 6.78 Cor Total 1076.72 31 The Model F-value of 9.52 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise.
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