In any case we reject h if s 2 is sufficiently less

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In any case, we reject H 0 if S 2 is sufficiently less than or sufficiently greater than X ̄ . 40
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Without specifying the population distribution, we can only use asymptotic analysis to derive a general test statistic in this example – so we hold off for now. Another way to generate a composite null (and alternative) is H 0 : 2 H 1 : 2 so the null is that either the Poisson variance holds or the variance is underdispersed (relative to the Poisson distribution). The alternative is overdispersion. 41
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Summary of Classical Hypothesis Testing 1. Choose the null and alternative. 2. Choose the size of the test (maximum probability of Type I error) you are willing to tolerate. 3. Choose a test statistic (often based on whether its distribution can be calculated, at least under the null hypothesis). 4. Choose a rejection rule based on the null and size of the test. 42
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