lec29 - Testing Hypothesis (Contd) Recall: In the previous...

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Unformatted text preview: Testing Hypothesis (Contd) Recall: In the previous lecture, . 021 is called the p-value 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 p-value (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: p-value 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 claimed-assumption 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 inter-arrival 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.

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lec29 - Testing Hypothesis (Contd) Recall: In the previous...

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