Chp15-Module 15 - Inference for Proportions - pv

Chp15-Module 15 - Inference for Proportions - pv - Module...

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Module 15 Inferences for Population Proportions Objectives: One should be able to • construction confidence intervals for population proportions • conduct hypothesis tests for population proportions • conduct inference studies on two population proportions Some Starting Vocabulary • Population proportion – the proportion of a population that has a specified characteristic. • Sample proportion – the proportion of a sample that has a specified characteristic. Sample Proportion The most common statistic used for estimating a population proportion, p, is the sample proportion defined by ˆ x p n = where x denotes the number of members in the sample having a specified characteristic and n is the sample size. Typical Assumptions ~( , ) XB i n o m i a l n p recall for a binomial distribution x np μ = and (1 ) x np p σ =− Recall that for large n ( ) ~, ( 1 ) X Nn p n p p μσ == The Normal distribution is a good approximation of the Binomial, i.e., It follows that 1( 1 ) ˆ p p pX N p nn ⎛⎞ = ⎜⎟ ⎝⎠

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Chp15-Module 15 - Inference for Proportions - pv - Module...

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