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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Chapter 9: Hypothesis Tests About the Mean and Proportion Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Mann E6 1/34
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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Two Hypotheses Rejection and Non-rejection Regions Two Types of Errors Tails of a Test General Test Procedures Two Hypotheses Definition (Null hypothesis) A null hypothesis is a statement (claim) about a population parameter that is assumed to be true until it is declared false. A null hypothesis is denoted by H 0 . Mann E6 2/34
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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Two Hypotheses Rejection and Non-rejection Regions Two Types of Errors Tails of a Test General Test Procedures Two Hypotheses Definition (Null hypothesis) A null hypothesis is a statement (claim) about a population parameter that is assumed to be true until it is declared false. A null hypothesis is denoted by H 0 . Definition (Alternative hypothesis) An alternative hypothesis is a statement (claim) about a population parameter that is true if the null hypothesis is false. An alternative hypothesis is denoted by H 1 or H A . Mann E6 2/34
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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Two Hypotheses Rejection and Non-rejection Regions Two Types of Errors Tails of a Test General Test Procedures Rejection and Non-rejection Regions Definition (Rejection region) Rejection region is a region in which we have enough evidence to declare that the null hypothesis is false. If H 0 is declared false, H 1 is true. Definition (Nonrejection region) Non-rejection region is a region in which we have no enough evidence to declare that the null hypothesis is false. If H 0 is not declared false, we will assume it to be true. Mann E6 3/34
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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Two Hypotheses Rejection and Non-rejection Regions Two Types of Errors Tails of a Test General Test Procedures Mann E6 4/34
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Hypothesis Tests: An Introduction Hypothesis Test about μ : σ Not Known Hypothesis Test about a Population proportion: Large Samples Two Hypotheses Rejection and Non-rejection Regions Two Types of Errors Tails of a Test General Test Procedures Two Types of Errors Definition (Type I Error) A Type I error occurs when a true null hypothesis is rejected. The value of α represents the probability of committing this type of error, that is, α = P ( H 0 is rejected | H 0 is true ) The true value of α represents the significance level of the test.
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