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stat332

# stat332 - Stat 322/332 Sampling and Experimental Design...

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Stat 322/332 Sampling and Experimental Design Assignment 2 Due: Wednesday, October 8, 2008 (12:30pm in class) 1. Consider the model for the balanced completely randomized design. Y ij = μ + τ i + R ij , R ij G (0 , σ ) , i = 1 , . . . , t, j = 1 , . . . , r Where i τ i = 0. Show that E ( i r ( ¯ Y i + - ¯ Y ++ ) 2 t - 1 ) = σ 2 + r i τ 2 i t - 1 . [Hint: First show that the numerator can be written as i r ( ¯ Y i + - ¯ Y ++ ) 2 = i r ¯ Y 2 i + - rt ¯ Y 2 ++ and then exploit the fact that for any random variable U , E ( U 2 ) = V ar ( U ) + ( EU ) 2 .] 2. Eight mice were randomly assigned to four diets, with two mice per diet. After six months liver damage ( Y ) was measured, giving the following data where higher numbers indicate more damage. Liver Diet damage Y Y 2 ¯ Y i + s 2 i 1 4.5 6.0 10.5 56.25 5.25 1.125 2 7.0 7.5 14.5 105.25 7.25 0.125 3 8.0 9.0 17.0 145.00 8.50 ? 4 10.0 9.5 19.5 190.25 9.75 ? 61.5 496.75 (1) Fill in the missing sample variances for diet 3 and 4. (2) Write down a model for the above data. It should have terms involving the treat- ment effects τ 1 , . . . , τ 4 . Carefully define all terms in the model, any assumptions and constraint.

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stat332 - Stat 322/332 Sampling and Experimental Design...

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