# final-2008 - Statistics 403 Exam 2 December 9, 2008...

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Statistics 403 Exam 2 December 9, 2008 Instructions: You may not use calculators, notes, books, formula cards, etc. If you are asked for a probability that cannot be calculated by hand, you can express your answer either in terms of normal probabilities (e.g. P ( Z < . . . ), P ( Z > . . . )), or in terms of R commands (e.g. pnorm(. ..) ). If your answer depends on a numerical value that you cannot calculate, deﬁne the value as a symbol (e.g. a = pnorm(-3) , or a = log(5/2) ) and use the symbol in your answer. Every problem is worth 15 points. Partial credit will be given. Express you answers clearly and show work where appro- priate. 1

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X i , Y i , for individuals i = 1 , .. . ,n , where X i and Y i represent pre-treatment and post-treatment measurements on an in- dividual. Our goal is to estimate ED , where D i = Y i - X i . For simplicity, assume that var( X i ) = var( Y i ) = 1, and EY i = 0. Also assume that EX i = μ and cor( X i , Y i ) = r . (a) What is the variance of ¯ D ? (b) Are ¯ D and ¯ Y - ¯ X always equal, sometimes equal, or never equal? Brieﬂy justify your answer. (c) Derive an expression for the power of detecting the alternative hypothesis
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## This note was uploaded on 02/06/2012 for the course STAT 403 taught by Professor Kerbyshedden during the Winter '12 term at University of Michigan-Dearborn.

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final-2008 - Statistics 403 Exam 2 December 9, 2008...

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