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# ch07 - CHAPTER 7 Notes to the Instructor The normal...

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CHAPTER 7 Notes to the Instructor: The normal probability plots are constructed in Minitab using the command ‘Normality Test’ under “Basic Statistics”. The analysis of variance is carried out using “ANOVA” under ‘Stat’ in Minitab. In cases where there are exactly two levels for each factor of interest, use “DOE” under ‘Stat’. Hierarchial models are used throughout. To use “Regression” to find an appropriate model, the interactions must be entered by hand. The data files on disk contain the design shown in each problem and columns for the corresponding interactions. Section 7-4 7-1. a) Predictor Coef StDev T P Constant 105.438 7.730 13.64 0.000 Material 9.313 7.730 1.20 0.252 Temp -33.938 7.730 -4.39 0.001 Mat*Temp 4.687 7.730 0.61 0.556 b) 1 -1 1 -1 145 135 125 115 105 95 85 75 65 55 Temp Material Mean Interaction Plot - Data Means for Life The interaction plot does not indicate a strong interaction between temperature and material. c) The t-ratios are given in the output shown in part a. The t-ratios indicate that temperature is significant, but material and the interaction material*temperature are not at the α = 0.05 level. d) The 95% confidence intervals are given by effect estimate ± 2(s.e.(effect)) where effect = 2(coefficient). The coefficient is given in the Minitab output of part a. s.e.(effect) = 2[s.e.(coefficient)]. The s.e.(coefficient) is given in the Minitab output of part a. Temperature: effect = 2(coefficient) = 2(-33.938) = -67.876 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval on the effect of Temperature: -67.876 ± 2(15.46) ( - 98.796, -36.956) Material: effect = 2(coefficient) = 2(9.313) = 18.626 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval for the effect of Material: 18.626 ± 2(15.46)

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(-12.294, 49.546) Material*Temperature: effect = 2(coefficient) = 2(4.687 )= 9.374 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval for the effect of Material*Temperature: 9.374 ± 2(15.46) ( - 21.546, 40.294) e) Life = 105 + 9.31 Material - 33.9 Temp + 4.69 Mat*Temp Predictor Coef StDev T P Constant 105.438 7.730 13.64 0.000 Material 9.313 7.730 1.20 0.252 Temp -33.938 7.730 -4.39 0.001 Mat*Temp 4.687 7.730 0.61 0.556 Based on the regression analysis, only temperature appears to be the significant factor. This result is equivalent to that obtained in part c. The final regression analysis and model are Life = 105 - 33.9 Temp Predictor Coef StDev T P Constant 105.438 7.680 13.73 0.000 Temp -33.938 7.680 -4.42 0.001 S = 30.72 R-Sq = 58.2% R-Sq(adj) = 55.3% Analysis of Variance Source DF SS MS F P Regression 1 18428 18428 19.53 0.001 Residual Error 14 13212 944 Total 15 31640 The analysis of variance indicates the final regression model is adequate for this set of data. This is evident by p-value = 0.001. 50 0 -50 2 1 0 -1 -2 Normal Score Residual Normal Probability Plot of the Residuals (response is Life)
1 0 -1 50 0 -50 Temp Residual Residuals Versus Temp (response is Life) There does not appear to be any serious departure from normality shown in the normal probability plot of the residuals. The assumption of constant variance does not appear to be violated. The residuals appear to have the same spread for both levels of Temperature.

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ch07 - CHAPTER 7 Notes to the Instructor The normal...

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