ams572_notes_3

# We have just discussed the rejection region approach

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We have just discussed the “rejection region” approach for decision making. There is another approach for decision making, it is “p-value” approach. *Definition: p-value – it is the probability that we observe a test statistic value that is as extreme, or more extreme, than the one we observed. Observed value of test statistic p-value p-value p-value (1) the area under N(0,1) pdf to the right of (2) the area under N(0,1) pdf to the left of (3) twice the area to the right of 7

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(1) (2) (3) 8
The way we make conclusions is the same for all hypotheses. “We reject in f avor of iff p-value” Any population, the population variance is unknown However – the sample size is large 5. the “large sample” scenario Thm The Central Limit Theorem Let be a random sample from a population with mean and variance * When n is large enough , (approximately) – by CLT and Slutsky’s Theorem 9

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It is the pivotal quantity ( P.Q. ) for The derivation of the hypothesis tests (rejection region and the p-value) are almost the same as the derivation of the exact Z-test discussed above.
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• Fall '10
• WeiZhu
• Statistical hypothesis testing, significance level, OJ

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