1 1 2 p p m z n n p p p N p p ˆ Comparing two independent samples We often need

1 1 2 p p m z n n p p p n p p ˆ comparing two

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( ) *) 1 ( * * ) 1 ( , ~ 2 p p m z n n p p p N p = p ˆ
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Comparing two independent samples We often need to compare 2 treatments used on independent samples. We can compute the difference between the 2 sample proportions and compare it to the corresponding, approximately normal sampling distribution for ( 1 2 ): p ˆ p ˆ
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Large-sample CI for two proportions For two independent SRSs of sizes n 1 and n 2 with sample proportion of successes 1 and 2 respectively, an approximate level C confidence interval for p 1 – p 2 is 2 2 2 1 1 1 2 1 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ * * error of margin the is , ) ˆ ˆ ( n p p n p p z SE z m m m p p diff + = = ± Use this method only when the populations are at least 10 times larger than the samples and the number of successes and the number of failures are each at least 10 in both samples. C is the area under the standard normal curve between z* and z*. p ˆ p ˆ
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