STATS 401 Study Guide - Midterm Guide: Null Hypothesis, Palt, Standard Deviation
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Due in lab, wednesday, march 17th: find two joint distributions corresponding to these marginal distributions: Solution: here are two solutions among in nitely many possible solutions: 0. 5: suppose we observe correlation coe cient r = 0. 6 based on sample size n = 20. Solution: r = log(1. 6/0. 4)/2 0. 69, so the ci on the transformed scale is 0. 69 . 1. 96/ scale yields 0. 21, 0. 82: suppose we observe 3 bivariate data points: (0, 0), (1, 1), (2, x). Calculate the correla- tion coe cient of these points as a function of x. Solution: x = 1, y = (x + 1)/3, x = 1, and y = is 2x, so the correlation is x2 x + 1). The covariance: suppose we are planning an experiment in which bivariate data will be collected. The null hypothesis is = 0, the alternative is > 0, and the null hypothesis is rejected if the p-value is less than 0. 05.
