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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 = 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 ( ). (b) Construct a 95% confidence interval for . 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) = + S E ( Y T | S = 0) = E ( Y U | S = 1) = 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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