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# q07_sol - ISyE2028A,Fall2010 SolutionstoQuiz7(versionA&B...

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ISyE2028A, Fall 2010 Solutions to Quiz 7 (version A & B) Version A: 1. Let 1 , , m X X  be a random sample from a normal distribution with variance 2 1 1 , let , , n Y Y  be another random sample (independent of the ' ) i X s from a normal distribution with variance 2 2 2 2 1 2 , and let and S S denote the two sample variances. Which of the following statement is not true? A. The random variable 2 2 2 2 1 1 2 2 ( / ) /( / ) F S S has an F distribution with parameters 1 2 1 and 1 m n B. The random variables 2 2 2 2 1 1 2 2 ( 1) / and ( 1) / m S n S each have a t distribution with m 1 and n 1 degrees of freedom, respectively. C. The hypothesis 2 2 1 2 : o H is rejected if the ratio of the sample variances differs by too much from 1. D. In testing 2 2 2 2 1 2 1 2 : versus : , o a H H the rejection region for a level , 1. 1 test is . m n f F ANSWER : B 2. Let 1 20 , , X X  be a random sample from a normal distribution with variance 2 1 1 25 , let , , Y Y  be another random sample (independent of the ' ) i X s from a normal distribution with variance 2 2 2 2 1 2 , and let and S S denote the two sample variances. Which of the following statement is not true in testing

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