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proportion_confidence_intervals

proportion_confidence_intervals - Proportion Estimation In...

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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?
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2 - Mike Pore - Feb 2004 The Bernoulli Data Data = {x} = {0, 0, 1, 1, 1, 1, 0, . . .} = " success " a " failure " a x 1 0 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 = - = = =
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3 - Mike Pore - Feb 2004 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 The Binomial Distribution ( 29 n r p p r n ) r ( P ) r y ( P ) p , n ( Binomial ~ y r n r - = = = - 0 1
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4 - Mike Pore - Feb 2004 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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
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5 - Mike Pore - Feb 2004 0 0.05 0.1 0.15 0.2 0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10 10.3 10.5 10.8 11 11.3 11.5 11.8 12 12.3 12.5 12.8 13 13.3 13.5 13.8 14 14.3 14.5 14.8 15 15.3 15.5 15.8 16 The Normal Approximation ( 29 ( 29 ( 29 p p n , np N ~ y p p n p n - - = σ = μ 1 1
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6 - Mike Pore - Feb 2004 Approximation criteria ( 29 5 p - 1 p n rules many of One : 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10 10.3 10.5 10.8 11 11.3 11.5 11.8 12 12.3 12.5 12.8 13 13.3 13.5 13.8 14 14.3 14.5 14.8 15 15.3 15.5 15.8 16 n = 16 p = .15 mean = 2.4 st. dev = ~4.5
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7 - Mike Pore - Feb 2004 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Proportions ( 29 n p 1 p ) p σ( p ) p E( n y p - = = = ˆ ˆ ˆ
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