Chapter21

# The Basic Practice of Statistics (Paper) & Student CD

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Comparing 2 proportions BPS chapter 21 © 2006 W.H. Freeman and Company

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Objectives (BPS chapter 21) Comparing two proportions The sampling distribution of a difference between proportions Large Sample confidence intervals for comparing two proportions Using technology Accurate confidence intervals for comparing two proportions Significance tests for comparing proportions
Comparing two independent samples p ˆ We often need to compare two treatments used on independent samples. We can compute the difference between the two sample proportions and compare it to the corresponding, approximately normal sampling distribution for ( 1 2 ): p ˆ p ˆ

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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 each sample. C is the area under the standard normal curve between
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Chapter21 - Comparing 2 proportions BPS chapter 21 2006...

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