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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11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations
Let 
and 
be random samples taken from two independent binomial populations with pX and pY representing the proportions of successes in the first and second binomial populations. In addition, let X and Y be independent random variables depicting the observed number of successes in the samples of sizes nX and nY, respectively. To test hypotheses regarding the differences in population proportions 
, we must review the characteristics of the sampling distribution of the difference between two sample proportions. (Remember that these tests are only approximate and hold only for large samples.)
We know that the best estimators for pX and pY are the sample proportions of successes 
, respectively, with
Hence the best estimator for pX − pY is 
; and the best estimators for and are, respectively, ...
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