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Unformatted text preview: Statistics 403 Exam 2 December 21, 2009 Instructions: • You may not use notes, books, formula cards, etc. • You may use a calculator, but only for arithmetic. • 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 you need a quantile, define it as a symbol (e.g. Q . 3 ) and give your answer in terms of the symbol. • Every problem is worth the same number of points. • Partial credit will be given. Express you answers clearly and show work where appro priate. 1 1. Suppose we are interested in the correlation between a person’s annual income I (in thousands of dollars), and the number of years Y between the person’s purchases of a new car. We have good data on Y , and can assume that it is measured exactly. However income is measured as I = I + E , where E is a random measurement error term with mean zero and variance τ 2 . Assume that the population correlation coefficient between I and Y is ρ = . 3, the standard deviation of I is 12, and the standard deviation of Y is 3. Also assume that E is uncorrelated with I and Y . (a) Let ˆ ρ denote the sample correlation coefficient between I and Y . Approximately what is the expected value ρ of ˆ ρ ?...
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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 MichiganDearborn.
 Winter '12
 KerbyShedden
 Statistics, Probability

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