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Unformatted text preview: Statistics: Hypothesis testing Definitions • We concentrate on simple hypotheses involving a single unknown population parameter θ . For example θ might be μ , the mean of a population, or σ , a population standard deviation, or β , the slope in a linear regression. Later we deal with more general hypotheses, including the testing of association, which may not involve parameters explicitly. • Parameters such as θ are unknown and often stay unknown. Usually, we have from the data an estimate for θ . Typically we have an idea of the probability distribution of the estimator, and we know the standard deviation of the estimator either exactly, or more commonly this too must be estimated from the data. • Suppose that r is a number. Simple (two sided) hypotheses are stated in the form H : θ = r H a : θ 6 = r . • Simple (one sided) hypotheses are stated in the following form H : θ = r or H : θ = r H a : θ &gt; r H a : θ &lt; r . • H denotes the null hypothesis, and H a the alternative hypothesis. The null hypothesis generally hypothesizes that the parameter is equal to a specific value (with some tolerance allowable), whereas the alternative hypothesis denies this. • In a given situation, choosing a one- or two-sided test is a matter of judgement. The alternative hypothesis should express the hopes or suspicions that we bring to the data. We will not deal further with one-sided tests. • When a (100- α )% confidence interval does not contain the hypothesized value, we reject the null hypothesis , and we find the test statistically significant at the α % level of significance. Otherwise we fail to reject the null hypothesis, and we find the test...
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.
- Spring '10