hw4ans - Statistics 500 Fall 2009 Solutions to Homework 4...

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Statistics 500 – Fall 2009 Solutions to Homework 4 1 1. Diet plans – no SAS (a) Source d.f. Sum of Squares Mean Square F Treatment 3 2272.80 757.60 34.33 Error 20 441.35 22.07 Total 23 2714.15 Note: remember that the total SS = treatment SS + error SS and total d.f. = treatment d.f. + error d.f. (b) 4 treatments. Note: treatment d.f. = r – 1. (c) There are 24 observations in total. If all groups have the sample size, there are 6 observations per treatment. Note: this only works if n’s are the same for all groups. If the n’s were unequal, the number observations in each group can not be determined from the ANOVA table. (d) 8.10 33 . 34 999 . 0 , 20 , 3 = > = F F . Therefore, we reject the null hypothesis that all means are equal. The p-value is < 0.001. There is very strong evidence that at least one mean is different. 2. Fixed or random effects. (a) Schools are random. There is no interest in a specific school. (b) Schools are fixed. You want to compare school A to each of the other 9 schools. (c) Schools are random. There is no interest in specific schools, but the variability among schools within a curriculum will be an important part of the analysis. Curriculum is fixed. You want to estimate differences between specific curriculums. 3. Bottle filling. My SAS code, without extra run commands: data bottle; infile ‘c:/philip/stat500/data/bottle.txt’; input fill machine; /* can ignore other two variables */ proc boxplot; plot fill*machine; proc gplot; /* hi resolution dot plots */ plot fill*machine; proc glm ; class machine; model fill = machine ; lsmeans machine / stderr pdiff cl ;
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Statistics 500 – Fall 2009 Solutions to Homework 4 2 estimate 'Contrast a' machine 0.25 0.25 - 0.5 - 0.5 0.25 0.25 ; estimate 'Contrast b' machine 0.5
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hw4ans - Statistics 500 Fall 2009 Solutions to Homework 4...

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