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420Hw04ans - STAT 420 Homework#4(10 points(due Friday...

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STAT 420 Fall 2008 Homework #4 (10 points) (due Friday, September 26, by 3:00 p.m.) 1. Hogg and Ledolter report on an engineer in a textile mill who studies the effects of temperature and time in a process involving dye on the brightness of a synthetic fabric ( brightness is measured on a 50-point scale ) . Three observations were taken at each combination of temperature and time. Temperature Time (cycles) 350 ° F 375 ° F 400 ° F 40 38, 32, 30 37, 35, 40 36, 39, 43 50 40, 45, 36 39, 42, 46 39, 48, 47 Construct the ANOVA table and conduct tests for the interaction first and then, if appropriate, the main effects. Use α = 0.05 for each test. [ R. V. Hogg and J. Ledolter, Applied Statistics for Engineers and Physical Scientists , 2nd ed. ( New York: Macmillan, 1992 ) . ] Brig <- c(38, 32, 30, 37, 35, 40, 36, 39, 43, 40, 45, 36, 39, 42, 46, 39, 48, 47) Time <- c( 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2) Temp <- c( 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3, 3) summary(aov(glm(Brig ~ factor(Time) * factor(Temp)))) Df Sum Sq Mean Sq F value Pr(>F) factor(Time) 1 150.222 150.222 9.6918 0.008968 ** factor(Temp) 2 80.778 40.389 2.6057 0.114863 factor(Time):factor(Temp) 2 3.444 1.722 0.1111 0.895749 Residuals 12 186.000 15.500 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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Y ijk = μ + β i + τ j + ( β τ ) ij + ε ijk , i = 1, 2, j = 1, 2, 3, k = 1, 2, 3. Interaction: H 0 : ( β τ ) 11 = ( β τ ) 12 = ( β τ ) 13 = ( β τ ) 21 = ( β τ ) 22 = ( β τ ) 23 = 0 . P-value = 0.895749 . Do NOT Reject H 0 at α = 0.05 . Time: H 0 : β 1 = β 2 = 0 . P-value = 0.008968 . Reject H 0 at α = 0.05 . Temperature: H 0 : τ 1 = τ 2 = τ 3 = 0 .
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