STATS 401 Study Guide - Midterm Guide: Type I And Type Ii Errors, Null Hypothesis, Normal Distribution
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Solution: t 5, |t 10| 5, and t 15. (b) corresponding to the three hypothesis tests above, suppose we observe as data 7 heads, 7 heads, and 17 heads, respectively. Solution: 0. 13, 0. 13 (d) repeat part c (right-tailed test only) using the normal approximation rather than the binomial table. In addition to p = 3/5, also calculate the power for p = 11/20 and p = 13/20. Solution: let t be the number of heads, and suppose that n is the sample size. Here are the means and standard deviations for t under both hypotheses. Standardizing t under the null gives us the following rejection region for the right-tailed test: which can be rewritten. ) p (z > 0. 76) where n = 20. The approximate power for the right-tailed test is 0. 22 (note that this is o by a factor of 2 relative to the true value).
