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# 420Hw10ans - STAT 420(10 points(due Friday November 9 by...

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STAT 420 Fall 2007 Homework #10 (10 points) (due Friday, November 9, by 3:00 p.m.) 1. An engineer is investigating the strength of concrete beams made from four types of cement and employing three curing processes. The breaking strengths are measured and are presented below. Curing Cement Type Process A B C D 1 14 6 22 10 2 15 8 20 7 3 10 7 18 7 a) List an appropriate model and the underlying assumptions for this situation. b) Construct the ANOVA table and test for differences in cement types and curing processes. Assume a 5-percent significance level. a) Y i j = μ + α i + β j + ε i j , i = 1, 2, 3, j = 1, 2, 3, 4, α 1 + α 2 + α 3 = 0, β 1 + β 2 + β 3 + β 4 = 0, ( Curing Process ) ( Cement Type ) ε i j are independent N ( 0, σ 2 ) random variables. b) > Str <- c(14, 6,22,10,15, 8,20, 7,10, 7,18, 7) > Cur <- c( 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3) > Cem <- c( 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4) > > summary(aov(glm(Str ~ factor(Cur) + factor(Cem)))) Df Sum Sq Mean Sq F value Pr(>F) factor(Cur) 2 14.00 7.00 2.625 0.1517037 factor(Cem) 3 318.00 106.00 39.750 0.0002361 *** Residuals 6 16.00 2.67 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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OR Curing CementType Process A B C D Mean 1 14 6 22 10 13 2 15 8 20 7 12.5 3 10 7 18 7 10.5 Mean 13 7 20 8 12 SS
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420Hw10ans - STAT 420(10 points(due Friday November 9 by...

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