proportion_confidence_intervals

proportion_confidence_intervals - 1 - Mike Pore - Feb 2004...

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Unformatted text preview: 1 - Mike Pore - Feb 2004 Proportion Estimation • In the last election, polls predicted the outcome with expressions like “the outcome will be 55% ± 3%.” • Will national elections require a larger sample size than a state election? • What does the ± 3% mean? • How do they do that? 2 - Mike Pore - Feb 2004 The Bernoulli Data Data = {x} = {0, 0, 1, 1, 1, 1, 0, . . .} = " success " a " failure " a x 1 P(x = 1) = P(1) = p P(x = 0) = P(0) = 1- p fails of number y n successes of number x y ns observatio of number n =- = = = ∑ 3 - Mike Pore - Feb 2004 0 . 0 5 0 .1 0 . 1 5 0 .2 0 . 2 5 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 The Binomial Distribution ( 29 n r p p r n ) r ( P ) r y ( P ) p , n ( Binomial ~ y r n r ≤ ≤- = = =- 1 4 - Mike Pore - Feb 2004 0 . 0 5 0 .1 0 . 1 5 0 .2 0 . 2 5 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 The Binomial Distribution ( 29 ( 29 ( 29 p np . dev . St p np ) y ( Var np y E- =- = = 1 1 n = 16 p = .6 mean = 9.6 st. dev = ~2 5 - Mike Pore - Feb 2004 0.05 0.1 0.15 0.2 0.25 . 2 5 . 5 . 7 5 1 1 . 2 5 1 . 5 1 . 7 5 2 2 . 2 5 2 . 5 2 . 7 5 3 3 . 2 5 3 . 5 3 . 7 5 4 4 . 2 5 4 . 5 4 . 7 5 5 5 . 2 5 5 . 5 5 . 7 5 6 6 . 2 5 6 . 5 6 . 7 5 7 7 . 2 5 7 . 5 7 . 7 5 8 8 . 2 5 8 . 5 8 . 7 5 9 9 . 2 5 9 . 5 9 . 7 5 1 1 . 3 1 . 5 1 . 8 1 1 1 1 . 3 1 1 . 5 1 1 . 8 1 2 1 2 . 3 1 2 . 5 1 2 . 8 1 3 1 3 . 3 1 3 . 5 1 3 . 8 1 4 1 4 . 3 1 4 . 5 1 4 . 8 1 5 1 5 . 3 1 5 . 5 1 5 . 8 1 6 The Normal Approximation ( 29 ( 29 ( 29 p p n , np N ~ y p p n p n-- = σ = μ 1 1 6 - Mike Pore - Feb 2004 Approximation criteria ( 29 5 p- 1 p n rules many of One ≥ : 0.05 0.1 0.15 0.2 0.25 0.30....
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This note was uploaded on 04/26/2010 for the course ECO 329 taught by Professor K during the Spring '08 term at University of Texas.

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proportion_confidence_intervals - 1 - Mike Pore - Feb 2004...

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