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class03_16 - 1.017/1.010 Class 16 Testing Hypotheses about...

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1.017/1.010 Class 16 Testing Hypotheses about a Single Population Formulating Hypothesis Testing Problems Hypotheses about a random variable x are often formulated in terms of its distributional properties. Example, if property is a : Null hypothesis H0: a = a 0 Objective of hypothesis testing is to decide whether or not to reject this hypothesis. Decision is based on estimator a of a : ˆ Reject H0: If observed estimate lies in rejection region R a ˆ R a 0 ( ) Do not reject H0: O therwise ( 0 ˆ a R a 0 ˆ a a ) Select rejection region to obtain desired error properties: Test Result Do not reject H0 0 ˆ a R a Reject H0 0 ˆ a R a H0 true P (H0|H0) =1 - α P (~H0|H0) = ( Type I Error ) True situation H0 false P (H0|~H0) = β ( Type II Error ) P (~H0|~H0) = 1- Type I error probability α is called the test significance level . Deriving Hypothesis Rejection Regions for Large Sample Tests Hypothesis test is often based on a standardized statistic that depends on unknown true property and its estimate. Basic concepts are the same
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class03_16 - 1.017/1.010 Class 16 Testing Hypotheses about...

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