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Unformatted text preview: Testing Hypothesis (Contd) Recall: In the previous lecture, . 021 is called the pvalue for testing the null hypothesis p = 0 . 5 against an alternative hypothesis p = 0 . 5 . Formal procedure: Let H : p = 0 . 5 v.s. H 1 : p = 0 . 5 then the test statistic is T = p . Observed value of test statistic is 9 / 10 , then the pvalue (the chance that my test statistic would be as extreme, in favor of the alternative hypothesis, as the observed value): P H ( T 9 / 10) = P ( T 9 / 10  H ) = 0 . 021 Inference: pvalue is very small (less than 0.05), indicating evidence for rejecting H . 1 How to set up testing hypothesis? Summary: Hypothesis testing is a formal procedure to check whether or not the claimedassumption can be rejected based on the given data. If we abstract the main elements, testing hypothesis usually involving five steps (this roadmap is proposed by R.A.Fisher). Example: University CC administrators have historical records that indicates that between August and Oct 2002 the mean time between hits on the ISU homepage was 2 min. They suspect that in fact the mean time between hits has decreased. They sample 50 interarrival times from records for November 2002 gives: x = 1 . 7 min and s = 1 . 9 min. Is this strong evidence for a decrease of mean time between hits? Solution: We following the five steps to answer this Step 1: State a null hypothesis of the form H : function of 2 parameter(s) = # meant to embody a status quo/ pre data view In the above example: H : = 2 . min between hits (i.e. no changes) Step 2: State an alternative hypothesis of the form H a : function of parameter(s) > = < # meant to identify departure from H In the above example: H a : < 2 (mean time decreases) Step 3: State test criteria consists of a test statistic, a reference distribution giving the behavior of the test statistic if...
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.
 Spring '11
 Zhou

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