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hw2 - MAT 3378 3X Spring 2010 Assignment 2 Deadline Friday...

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MAT 3378 3X - Spring 2010 Assignment 2 : Deadline: Friday, June 25 (In Class) Question 1: Suppose that five normal populations have a common variance of σ 2 = 100 (a) The means are μ 1 = 175, μ 2 = 190, μ 3 = 160, μ 4 = 200, μ 5 = 215. Assuming a balanced design of n = 5 observations per population. What is the power of the test for equality of means with a level of significance of 1%? Hint: Compute the non-centrality parameter. (b) The means are μ 1 = 175, μ 2 = 190, μ 3 = 160, μ 4 = 200, μ 5 = 215. Assuming a balanced design how many observations per population must be taken so that the probability of rejecting the hypothesis of equality of means is at least 0.95? Use α = 0 . 01. (c) Suppose that range in the means is max { μ i } - min { μ i } = 40. Assuming a balanced design, how many observations per population must be taken so that the probability of rejecting the hypothesis of equality of means is at least 0.95? Use α = 0 . 01. Question 2: Consider the one factor ANOVA model Y ij = μ i + ij where ij are independent N (0 , σ 2 ) for i = 1 , . . . , r and j = 1 , . . . , n i .
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