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# practice_exam2 - Statistics 403 Practice Exam Questions for...

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Unformatted text preview: Statistics 403 Practice Exam Questions for Exam 2 • I have not included practice problems that are very similar to the homework problems, so you should study those too, along with the solutions to the first midterm. • 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 involves logarithms or exponential functions, you can leave the answer in terms of log and exp. In general, you do not need to simplify your answers unless a numerical value is required to answer a specific part of the question. 1. Suppose we observe a sample correlation coefficient ˆ ρ = 0 . 4 (0 . 42 on the Fisher trans- form scale) based on a sample size of n = 20. (a) Construct a 95% confidence interval for f ( ρ ). (b) Construct a 95% confidence interval for ρ . 2. Suppose we collect outcome data on n T treated individuals and n U untreated individ- uals in a comparative study. Our interest is the difference in expected response due to the treatment, so we focus on the statistic D ≡ ¯ Y T- ¯ Y U , where ¯ Y T and ¯ Y U are the sample means for the treated and untreated subsamples, respectively. Suppose that a binary confounding factor S is present but is not observed. The expected responses for a single treated unit Y T and a single untreated unit Y U are as follows: E ( Y T | S = 1) = α + β S E ( Y T | S = 0) = α E ( Y U | S = 1) = β S E ( Y U | S = 0) = 0 (a) Suppose we use the two-sample Z-test to compare the treated and untreated...
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practice_exam2 - Statistics 403 Practice Exam Questions for...

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