ch13 - CHAPTER 13 Section 13-2 13-1. a) Analysis of...

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CHAPTER 13 Section 13-2 13-1. a) Analysis of Variance for STRENGTH Source DF SS MS F P COTTON 4 475.76 118.94 14.76 0.000 Error 20 161.20 8.06 Total 24 636.96 Reject H 0 and conclude that cotton percentage affects mean breaking strength. 35 30 25 20 15 5 COTTON STRENGTH b) Tensile strength seems to increase up to 30% cotton and declines at 35% cotton. Cotton Percentage Mean Strength 35 30 25 20 15 22 20 18 16 14 12 10 Scatterplot of Mean Strength vs Cotton Percentage Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+ 15 5 9.800 3.347 (-----*----) 20 5 15.400 3.130 (----*----) 25 5 17.600 2.074 (----*----) 30 5 21.600 2.608 (----*----) 35 5 10.800 2.864 (-----*----) ------+---------+---------+---------+ Pooled StDev = 2.839 10.0 15.0 20.0 25.0 c) The normal probability plot and the residual plots show that the model assumptions are reasonable. 13-1
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20 15 10 6 5 4 3 2 1 0 -1 -2 -3 -4 Fit ed Value Residual Residuals Versus the Fitted Values (response is STRENGTH) 2 1 0 6 5 4 3 2 1 0 Normal Score Normal Probability Plot of the Residuals (response is STRENGTH) 35 25 15 6 5 4 3 2 1 0 COTTON Residuals Versus COTTON (response is STRENGTH) 3-2 a) Analysis of Variance for FLOW Source DF SS MS F P FLOW 2 3.6478 1.8239 3.59 0.053 Error 15 7.6300 0.5087 Total 17 11.2778 Do not reject H 0 . There is no evidence that flow rate affects etch uniformity. 200 160 125 5 4 3 FLOW UNIFORMIT b) Residuals are acceptable. -1 0 1 -2 -1 0 1 2 Residual Normal Probability Plot of the Residuals (response is obs) 13-2
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200 190 180 170 160 150 140 130 120 1 0 -1 FLOW Residual Residuals Versus FLOW (response is UNIFORMI) 4.5 4.0 3.5 1 0 Fitted Value Residuals Versus the Fitted Values (response is UNIFORMI) 13-3. a) Analysis of Variance for STRENGTH Source DF SS MS F P TECHNIQU 3 489740 163247 12.73 0.000 Error 12 153908 12826 Total 15 643648 Reject H 0 . Techniques affect the mean strength of the concrete. b) P-value 0 c) Residuals are acceptable 4 3 2 1 200 100 0 -100 -200 TECHNIQU Residuals Versus TECHNIQU (response is STRENGTH) 3150 3050 2950 2850 2750 2650 200 100 0 -200 -100 0 100 200 -2 -1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is STRENGTH) 13-3
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13-4 a) Analysis of Variance for TEMPERATURE Source DF SS MS F P TEMPERAT 3 0.1391 0.0464 2.62 0.083 Error 18 0.3191 0.0177 Total 21 0.4582 Do not reject H 0 b) P -value = 0.083 c) Residuals are acceptable 180 170 160 150 140 130 120 110 100 0.2 0.1 0.0 -0.1 -0.2 TEMPERAT Residual Residuals Versus TEMPERAT (response is DENSITY) 21.75 21.65 21.55 0.2 0.1 0.0 Fit ed Value Residuals Versus the Fitted Values (response is DENSITY) -0.2 -0.1 0.0 0.1 0.2 -2 -1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is density) 13-5. a) Analysis of Variance for CONDUCTIVITY Source DF SS MS F P COATINGTYPE 4 1060.5 265.1 16.35 0.000 Error 15 243.3 16.2 Total 19 1303.8 Reject H 0 , P -value 0 13-4
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b) There is some indication of that the variability of the response may be increasing as the mean response increases. There appears to be an outlier on the normal probability plot. 5 4 3 2 1 5 0 -5 -10 COATINGT Residual Residuals Versus COATINGT (response is CONDUCTI) 145 140 135 130 5 0 Fit ed Value Residuals Versus the Fitted Values -10 -5 0 5 -2 -1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is CONDUCTI) c) 95% Confidence interval on the mean of coating type 1 29 . 149 71 . 140 4 2 . 16 131 . 2 00 . 145 4 2 . 16 131 . 2 00 . 145 1 1 15 , 015 . 0 1 15 , 025 . 0 1 + + µ n MS t y n MS t y E i E 99% confidence interval on the difference between the means of coating types 1 and 4.
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ch13 - CHAPTER 13 Section 13-2 13-1. a) Analysis of...

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