July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short CourseBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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11.3 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations
Let 
and 
be random samples drawn from two independent binomial populations, where pX and pY are the proportions of successes in the first and second binomial populations, respectively. Additionally, let X and Y be independent random variables representing the observed number of successes in the samples of size nX and nY, respectively.
To determine a 100(1 − α)% confidence interval for the difference in proportions 
, let us first discuss the characteristics of the sampling distribution of the difference between two sample proportions. We found in Section 9.1 that the best estimators for pX and pY are the sample proportions or observed relative frequencies of successes 
and 
, respectively, with
Hence the best estimator for pX − pY is ; and the best estimators for and are, respectively, ...
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