Quiz5 - Quiz 5 We have two independent samples 1 2 1 1 1 ,...

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Unformatted text preview: Quiz 5 We have two independent samples 1 2 1 1 1 , , ~ ( , ) iid n X X N K and 2 2 1 2 2 , , ~ ( , ) iid n Y Y N K , where 2 2 2 1 2 = = and 1 1 n n n = = . For the hypothesis of 1 2 1 2 : : a H H - = - = < a) Please derive the general formula for power calculation for the pooled variance t-test based on an effect size of EFF = at the significance level of and with a sample size of n per group. Recall - Definition: Effect size = EFF = b) With a sample size of 15 per group, = 0.05, and an estimated effect size of -1.5, please calculate the power of your pooled variance t-test. Solution: a) T.S : T = 2 2 1 2 ( ) ( ) ~ 1 1 2 H n p p X Y X Y t S S n n n---- = + At =0.05, reject H in favor of a H iff 2 2, n T t - - Power = 1- = P(reject H | a H ) = 2 2, 1 2 ( | : 0) n a P T t H - -- = < = 2 2, 1 2 ( ) ( | : ) 2 n a p X Y P t H S n -- -- = = 2 2, 1 2 ( ) ( | : ) 2 2 n a p p X Y P t H...
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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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Quiz5 - Quiz 5 We have two independent samples 1 2 1 1 1 ,...

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