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Unformatted text preview: fail to reject it. Probability = β . Power= 1 − β . This depends on the unknown population parameter. Have limited control over this. Utku Suleymanoglu (UMich) Hypothesis Testing 6 / 39 Null and Alternative Hypotheses Trial Analogy Reality Verdict INNOCENT (H0 ) GUILTY Reject (Verdict=Guilty) H0 Type I Error Correct Fail to Reject (Verdict= Not Guilty) H0 Correct Type II Error We set a high standard for convicting people. We assume innocence, then try to find evidence to reject this presumption. We do the same for null hypothesis as well: unless there is a lot of evidence, we do not reject it. Type I error: Innocent man gets the chair, Type II error: Murderer walks away. Society and statisticians try to minimize the probability of Type I error first, and demand a lot evidence to reject an H0 . Key thing: If we fail to reject H0 , we don’t say “we proved H0 ”, we just don’t have enough evidence against it. Analogy: if the defendant walks away, his innocence has not been proven, instead: his guilt has not been proven with enough evidence. Utku Suleymanoglu (UMich) Hypothesis Testing 7 / 39 Null and Alternative Hypotheses General Testing Procedure TEST PROCEDURE: 1 Formulate and state null and alternative hypothesis. 2 (Select a significance level: α) 3 Calculate a suitable test statistic using available sample statistics to use in conjuction with. . . 4 (Develop and) Use a decision rule to make a call about H0 . You don’t need to develop it everytime but this is how it works: (a) Assume the null hypothesis is valid. (b) Figure out the sampling distribution of the sample statistic under the assumption is null hypothesis correct. (c) Figure the distribution of the test statistic under the null. (d) Select a criteria that uses probability distribution of the test statistic to reject or fail to reject the null hypothesis. The criteria uses α as a tolerance level. 5 State your conclusion on the null hypothesis. Utku Suleymanoglu (UMich) Hypothesis Testing 8 / 39 Testing Hypothes...
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