ams572_notes_3

ams572_notes_3 - AMS 572 Lecture Notes #3 Sept. 17, 2010....

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AMS 572 Lecture Notes #3 Sept. 1 7 , 2010. One-sample Inference on Population Mean When the population i s normal, and the population variance known Data : <iii> Hypothesis test Example: (null hypothesis) (alternative hypothesis) : This is usually your hypothesis if you are conducting the test. Very similar to a law suit: e.g) The famous O.J. Simpson trial : OJ is innocent : OJ is guilty The truth : OJ innocent OJ guilty Jury’s Right decision Type II error 1
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Decision Type I error Right decision 2
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The significance level and three types of hypotheses . P(Type I error) = α ← significance level of a test (*Type I error rate) 1. 2. 3. Now we derive the hypothesis test for the first pair of hypotheses. Data : is known and the given a significance level α (say, 0.05). Let’s derive the test. (That is, derive the decision rule) Two approaches (*equivalent): - Likelihood Ratio Test - Pivotal Quantity Method ***Now we will first demonstrate the Pivotal Quantity Method.
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This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.

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ams572_notes_3 - AMS 572 Lecture Notes #3 Sept. 17, 2010....

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