# Math160.Section8.2.pdf - Math A160 - Cooley Introduction to...

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Math A160 - CooleyIntroduction to StatisticsOCCSECTION 8.2 – Distribution of the Sample Proportion- 1 -DefinitionSuppose that a random sample of sizenis obtained from a population in which each individual either does ordoes not have a certain characteristic. The sample proportion, denotedˆp(read “p-hat”), is given byˆp=xnwherexis the number of individuals in the sample with the specified characteristic. The sample proportion,ˆp,is a statistic that estimates the population proportion,p.Sampling Distribution ofˆpFor a simple random sample of sizenwith a population proportionp,The mean of the sampling distribution ofˆpisµˆp=p.The standard deviation of the sampling distribution ofˆpisˆ(1)pppnσ=.The shape of the sampling distribution ofˆpis approximately normal providednp(1 –p)10.Note:We also require that the sampled values must be independent of each other; that is, one outcome cannotaffect the success or failure of any other outcome. So, when sampling from finite populations, thismeans that the sample size can be no more than 5% of the population size (n0.05N).

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