assign2 - PSTAT 120C: Assignment 2 Due April 16, 2009 1....

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PSTAT 120C: Assignment 2 Due April 16, 2009 1. This is the problem from last week. (Exercise 10.105 on page 554 in WMS .) Let Y 1 ,...,Y n denote a random sample from a normal distribution with mean μ (unknown) and variance σ 2 . For testing H 0 : σ 2 = σ 2 0 against H A : σ 2 > σ 2 0 , show that the likelihood ratio test is equivalent to the χ 2 test with critical region C = ± S 2 ( n - 1) σ 2 0 > χ 2 α ² where χ 2 α is the α critical value for a χ 2 distribution with n - 1 degrees of freedom. 2. Suppose that we have two independent binomial random variables X Binomial( n,p x ) and Y Binomial( m,p y ). (a) Find the MLE for p under the assumption that p = p x = p y . (b) Find the likelihood ratio, λ , for testing H 0 : p x = p y vs. H a : p x 6 = p y . (c) Evaluate the value of this statistic if n = 378, X = 95, m = 432, and Y = 123. 3. A survey of voters was seeking to find out if their was any difference between the economic characteristics of Democrats and Republicans. The 58 Democrats in the survey had an average
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.

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assign2 - PSTAT 120C: Assignment 2 Due April 16, 2009 1....

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