hw8_solutions

hw8_solutions - STAT 3022, April 28, 2009 TA: Jinghan Meng...

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STAT 3022, April 28, 2009 TA: Jinghan Meng Homework 8 Solutions Ex 13.14 (a) Based on the given p-value, all three effects are significant at α = 0 . 05. (b) In order to summarize the results, we would need to know the number of levels for each factor( I and J ) and the sample sizes in each cell ( n ij ). We also would want to know the sample cell means ¯ x ij so that we could interpret the significant main effects and the nature of the interaction. Ex 13.18 Pooling is reasonable, as the largest standard deviation is 2.16, the smallest is 1.42, and 2 . 16 / 1 . 42 = 1 . 52 < 2. If we assume that all sample sizes in each cell ( n ij ) were equal, the pooled standard deviation is s p = v u u t I i =1 J j =1 ( n ij - 1) s 2 ij I i - 1 J j - 1 ( n ij - 1) = s I i =1 J j =1 s 2 ij I × J = r (1 . 63) 2 + (1 . 42) 2 + (1 . 52) 2 + (1 . 64) 2 + (2 . 16) 2 + (1 . 59) 2 2 × 3 = 1 . 6767 Ex 13.25 (a) Here are the R codes to compute the mean and standard deviation for each of the material-by-time combinations. > ex13.25 <- read.table("D:/PC-Text/ch13/ex13_025.txt",header=T) > attach(ex13.25)
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hw8_solutions - STAT 3022, April 28, 2009 TA: Jinghan Meng...

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