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q07_sol - ISyE 2028A Summer 2010 1 Let X 1 X m be a random...

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ISyE 2028A, Summer 2010 Friday July 16 Quiz 7 Solutions 1. Let 1 , , m X X  be a random sample from a normal distribution with variance 2 1 1 , let , , n Y Y σ  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 σ 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 σ σ = has an F distribution with parameters 1 2 1 and 1 m n ν ν = = B. The random variables 2 2 2 2 1 1 2 2 ( 1) / and ( 1) / m S n S σ σ each have a t distribution with m -1 and n -1 degrees of freedom, respectively. C. The hypothesis 2 2 1 2 : o H σ σ = 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 σ σ σ σ = > the rejection region for a level , 1. 1 test is . m n f F α α ANSWER: B

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q07_sol - ISyE 2028A Summer 2010 1 Let X 1 X m be a random...

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