hmk10_Q1_sol

# hmk10_Q1_sol - OR2700 HW#10 Solution to Q1 Fall 2008...

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OR2700 HW#10 Solution to Q1 Fall 2008 Answers to Q2 on separate Word document. 1(a) 2 k design with k = 3 factors and n = 3 replications. Treatment combination x 1 x 2 x 3 ¯ Y S 2 (0) - - - 105 133 a + - - 204 76 b - + - 194.67 76.33 ab + + - 322.33 177.33 c - - + 151 292 ac + - + 236.67 212.33 bc - + + 245.67 186.33 abc + + + 369 151 (b) A = 1 2 - 105 + 204 - 194 . 67 + 322 . 55 - 151 + 236 . 67 - 245 . 67 + 369 4 ± = 54 . 46 AC = 1 2 +105 - 204 + 194 . 67 - 322 . 33 - 151 + 236 . 67 - 245 . 67 + 369 4 ± = - 2 . 208 Variance of each eﬀect and interaction is σ 2 / ( n 2 k ) = σ 2 / 24. We estimate σ 2 by the average of the S 2 ’s over the eight vertices of the design cube, namely: ˆ σ 2 = 1 8 { 133 + 76 + ... + 151 } = 163 . 04 = (12 . 77) 2 So the standard error of all main eﬀects and interactions (including A and AC) is p 163 . 04 / 24 = 2 . 61. For testing H 0 : Main eﬀect of A = 0. Use t = 54 . 46 / 2 . 61 = 20 . 89. Degrees of freedom = 2 k (3 - 1) = 16 Highly signiﬁcant — P = 0.000.

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hmk10_Q1_sol - OR2700 HW#10 Solution to Q1 Fall 2008...

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