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Unit 12-2

# Unit 12-2 - Two-Sample Two-Sample Proportions Inference...

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Two-Sample Two-Sample Proportions Proportions Inference Inference

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Sampling Distributions for the Sampling Distributions for the difference in proportions difference in proportions   When tossing pennies, the probability of the coin landing on heads is 0.5.  However,  when spinning the coin, the probability of the coin landing on heads is 0.4.  Let’s  investigate. Pairs of students will be given pennies and assigned to either  Looking at the sampling distribution of the difference in sample Looking at the sampling distribution of the difference in sample proportions: proportions: What is the mean of the difference in sample proportions (flip - spin)? What is the standard deviation of the difference in sample proportions (flip - spin)? Can the sampling distribution of difference in sample proportions (flip - spin) be  approximated by a normal distribution? 1 . 0 ˆ ˆ = - s f p p μ 14 . 0 ˆ ˆ = - s f p p σ Yes, since n 1 p 1 =12.5, n 1 (1-p 1 )=12.5, n 2 p 2 =10, n 2 (1-p 2 )=15 – so all are at least 5)
Assumptions: Assumptions: Two Two independent independent  SRS’s from populations Population s  at least 10n Normal approximation for both ( 29 5 1 5 1 1 1 1 - p n p n ( 29 5 1 5 2 2 2 2 - p n p n

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Formula for confidence interval: Formula for confidence interval: ( 29 statistic of SD value critical statistic CI ± = ( 29 ± - 2 1 ˆ ˆ p p * z ( 29 ( 29 2 2 2 1 1 1 ˆ 1 ˆ ˆ 1 ˆ n p p n p p - + - Note: use p-hat when p is not known Standard error! Margin of error!
Example 1:   At Community Hospital, the burn center is  experimenting with a new plasma compress treatment.  A  random sample of 316 patients with minor burns received the  plasma compress treatment.  Of these patients, it was found that

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