# BinHypT - Left tailed test H 0 : p = p0 vs. H 1 : p < p0 If...

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Left – tailed test H 0 : p = p 0 vs. H 1 : p < p 0 If H 0 is TRUE : Use p 0 . Reject H 0 Do NOT Reject H 0 Type I Error α Correct decision 0 a a + 1 n Rejection Rule for a Left – tailed test: Find a such that P ( Y a ) = CDF @ a α . ( using Binomial ( n , p 0 ) tables ) Then the Rejection Rule is “Reject H 0 if Y a .” If Rejection Rule is “Reject H 0 if Y a ,” P( Type I error ) = P( Reject H 0 | H 0 true ) = P( Y a | p = p 0 ) = CDF @ a ( using Binomial ( n , p 0 ) tables ) If H 0 is FALSE : Use new (given) p . Reject H 0 Do NOT Reject H 0 Correct decision Power Type II Error 0 a a + 1 n Power = P( Reject H 0 ) = P( Y a ) = CDF @ a ( using Binomial ( n , new p ) tables ) p-value = P( value of Y as extreme or more extreme than Y = y observed | H 0 true ) = P( Y y observed | p = p 0 ) = CDF @ y observed ( using Binomial ( n , p 0 ) tables )

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Right – tailed test H 0 : p = p 0 vs. H 1 : p > p 0 If H 0 is TRUE : Use p 0 . Do NOT Reject
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## This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.

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BinHypT - Left tailed test H 0 : p = p0 vs. H 1 : p < p0 If...

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