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Section8.1posted

# Section8.1posted - STOR 155 Section 2 Tuesday Section 8.1...

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STOR 155, Section 2 Tuesday, April 20, 2010 Section 8.1

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8.1 Inference for a proportion Recall the situation (the binomial setting ): Population of individuals in two categories, or experiment with two outcomes that can be repeated independently under identical conditions. The categories or outcomes are labeled “S” and “F”. p (an unknown parameter) is the proportion of individuals in category S in the population, or the probability of outcome S . In a SRS of size n, or in n independent trials of the experiment, X is the count of S’s and p = X/n is the proportion of S’s. From Section 5.1: X has mean np and standard deviation np ( 1-p ). p has mean p and standard deviation p ( 1-p )/ n. X and p are approximately Normal if np 10 and n ( 1-p ) 10. Inferences we want to make, based on the observed value of p : Confidence intervals for p Significance Tests of H 0 : p = p 0 vs. H a : p p 0 or p < p 0 or p > p 0 ^ ^ ^ ____ _____ ^
8.1 Inference for a proportion: Confidence intervals for p Since p is approximately Normally distributed with mean p and standard deviation p ( 1-p )/ n , the probability is approximately 95% that p is between p ± 1.96 p ( 1-p )/ n .

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