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Asymmetric rules are sometimes preferred when testing

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Asymmetric rules are sometimes preferred when testing hypotheses about a parameter that must be strictly postive: 0. 22
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EXAMPLE : Suppose in a Normal ,1 population, we want to test H 0 : 0 against H 1 : 0. We can obtain a random sample of size of size n . We have an unbiased estimator of , X ̄ . It seems reasonable to base the rejection rule on how large X ̄ is. Let x ̄ denote the average for the actual data we observe. If we get x ̄ 0, that is no evidence against H 0 : 0. 23
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