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# Assign7 - PSTAT 120C Assignment 7 Please turn in this assignment at the beginning of lecture next Thursday Due June 1 2006 1 We want to find the

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PSTAT 120C: Assignment # 7 Due June 1, 2006 Please turn in this assignment at the beginning of lecture next Thursday. 1. We want to ﬁnd the expected value of the F statistic under the alternative hypothesis in the one-way ANOVA. Suppose that each Y i,j ∼ N ( μ i , σ 2 ) and they are all independent. Let ¯ y i be the mean of the n i observations in the i th group. Let ¯ y be the mean of all n observations. (a) Show that ¯ y i - ¯ y = 1 n k X ` =1 n ` y i - ¯ y ` ) and then that ¯ y i - ¯ y = ± n - n i n ² ¯ y i - 1 n X ` 6 = i n ` ¯ y ` . (b) Use the result from question 1a) to show that Var(¯ y i - ¯ y ) = ± n - n i n ² σ 2 n i . (c) The numerator of the F statistic is 1 k - 1 k X i =1 n i y i - ¯ y ) 2 . Calculate its expected value in terms of σ 2 , μ = E y ), and the k means μ i = E y i ). (Note: μ = 1 n n i μ i .) (d) Use the answer from the above calculation to calculate the expectation of the F statistic. 2. Complete these ANOVA tables and decide whether or not you would reject the null hypothesis

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## This note was uploaded on 04/09/2008 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.

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Assign7 - PSTAT 120C Assignment 7 Please turn in this assignment at the beginning of lecture next Thursday Due June 1 2006 1 We want to find the

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