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Unit 11-2 - Inference on Proportions Assumptions SRS Normal...

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Inference on Proportions
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Assumptions: SRS Normal distribution np > 10 & n(1-p) > 10 Population is at least 10n
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Formula for Confidence interval: ( 29 statistic of SD value critical statistic CI ± = p ˆ ± ( 29 - n p p 1 * z Normal curve Note: For confidence intervals, we DO NOT know p – so we MUST substitute p-hat for p in both the SD & when checking assumptions.
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A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.
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Assumptions: Have an SRS of adults np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both are greater than 10, the distribution can be approximated by a normal curve Population of adults is at least 10,1012. ( 29 ( 29 41 ,. 35 . 1012 ) 62 (. 38 . 96 . 1 38 . 1 * ˆ = ± = - ± n p p z P We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.
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