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

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Testing Hypothesis (Cont’d) Recall: In the previous lecture, 0 . 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 0 : p = 0 . 5 v.s. H 1 : p ̸ = 0 . 5 then the test statistic is T = ˆ 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 0 ( T 9 / 10) = P ( T 9 / 10 | H 0 ) = 0 . 021 Inference: p-value is very small (less than 0.05), indicating evidence for rejecting H 0 . 1
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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 0 : function of 2
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parameter(s) = # meant to embody a status quo/ pre data view In the above example: H 0 : μ = 2 . 0 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 0 In the above example: H a : μ < 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 H 0 is true and the
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