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STAT212inferenceforpopulation

# STAT212inferenceforpopulation - Inference for population...

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Inference for population proportions- one and two sample analysis of data on categorical variables. E.g. percent of Virginians who favor Issue X. - Population proportion of successes denoted by p. - Sample success count is denoted by X. - Sample proportion p^= X/n (p^ is used to estimate p.) Mean: µp= p. Standard deviation ∂= √p(1-p/n. If n is large, the distribution is approximately normal as long as npo ≥ 15 and n(1-po) ≥ 15 Test statisic- z= p^ - po/√po(1-po)/n Confidence interval for p= p^ +- z √p^(1-p^)/n The true ∂= √p(1-p)/n. The test statistic in hypothesis test uses po and the confidence interval uses p^. One sample plus-four confidence interval (pretend that sample size is 4 bigger than it is) P~ +- z√p~(1-p~)/n+4 where p~= X+2/n+4 (Valid if n ≥10) N= (z*/m)^2 p*(1-p*) where p* is an educated of the true p. A conservative setting is p*= 0.5 which yields a larger than other p* values. Two independent samples- - Mean: µ (p^1-p^2)= p1 – p2 - Standard deviation ∂ (p^1-p^2)= √p1(1-p1)/n1 + p2(1-p2)/n2

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