sample evidence is insufficient to reject g1834 g2868 at g2009g340405 Since the

Sample evidence is insufficient to reject g1834 g2868

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sample evidence is insufficient to reject g1834 g2868 at g2009g3404.05 . Since the null hypothesis is the “status-quo” hypothesis, the effect of not rejecting g1834 g2868 is to maintain the status quo.
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The Elements of a Test of Hypothesis The table above summarizes the 4 possible outcomes of a test of hypothesis. Note that a Type I error can be made only when the null hypothesis is rejected and a Type II error can be made only when the null hypothesis is accepted. Conclusion g2164 g2777 true g2164 g2183 true Accept g1834 g2868 Correct decision Type II error (probability g2010 ) Reject g1834 g2868 Type I error (probability g2009 ) Correct decision
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The Elements of a Test of Hypothesis Our policy will be to make a decision only when we know the probability of making the error that corresponds to that decision Because g2009 is usually specified by the analyst, we will generally be able to reject g1834 g2868 when the sample evidence supports that decision. However, since g2010 is usually not specified, we will generally avoid the decision to accept g1834 g2868 , preferring instead to state that the sample evidence is insufficient to reject g1834 g2868 when the test statistic is not in the rejection region
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The Elements of a Test of Hypothesis The elements of a test of hypothesis are summarized as follows (note that the first 4 must be specified before the experiment is performed): 1. Null hypothesis ( g1834 g2868 ): A theory about the specific values of one or more population parameters. The theory generally represents the status quo, which we adopt until it is proven false. The theory is stated as g1834 g2868 : parameter=value 2. Alternative hypothesis ( g1834 g3028 ): A theory that contradicts the null hypothesis. The theory generally represents that which we will adopt only when sufficient evidence exists to support it.
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The Elements of a Test of Hypothesis The elements of a test of hypothesis are summarized as follows (note that the first 4 must be specified before the experiment is performed): 3. Test statistic: A sample statistic used to decide whether to reject the null hypothesis. 4. Rejection region: The numerical values of the test statistic for which the null hypothesis will be rejected. The rejection region is chosen so that the probability is g2009 that it will contain the test statistic when the null hypothesis is true . The value of g2009 is usually chosen to be small and is referred to as the level of significance of the test
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The Elements of a Test of Hypothesis The elements of a test of hypothesis are summarized as follows: 5. Assumptions: Clear statements of any assumptions made about the population being sampled. 6. Experiment and calculation of test statistic: Performance of the sampling experiment and determination of the numerical value of the test statistic.
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The Elements of a Test of Hypothesis The elements of a test of hypothesis are summarized as follows: 7. Conclusion: a. If the numerical value of the test statistic falls in the rejection region, we reject the null hypothesis. We know that the hypothesis-testing process will lead to this conclusion (Type I error) 100α% of the time
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