100bHW6 - STAT 100B HWVI Problem 1: Let X1 , ., Xn N(1 , 2...

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STAT 100B HWVI Problem 1: Let X 1 ,...,X n N( μ 1 2 ) independently, and Y 1 ,...,Y m N( μ 2 2 ) independently. X 1 ,...,X n and Y 1 ,...,Y m are independent. (1) Suppose we want to test H 0 : μ 1 = μ 2 versus H 1 : μ 1 6 = μ 2 . Derive the likelihood ratio test. (2) Suppose X 1 ,...,X n are 4.8133 5.7258 4.4117 7.1832 4.8636 5.1139 6.0668 5.0593 4.9044 4.1677 Y 1 ,...,Y m are 5.7944 4.1638 6.2143 7.1236 4.8082 6.3580 6.7540 3.9063 4.0590 6.0711 Please calculate the p-value for the above test. Problem 2: Let Y i N( a + bx i 2 ) independently for i = 1 ,...,n , where x i are known. Suppose we want to test H 0 : b = 0 versus H 1 : b 6 = 0. Derive the likelihood ratio test.
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This note was uploaded on 03/30/2011 for the course STAT 100B taught by Professor Wu during the Winter '11 term at UCLA.

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