ai.Sampling Distributions (proportion, mean) - 1 Sampling Distributions The Fundamental Building Blocks of Statistical Analysis Sampling distributions

ai.Sampling Distributions (proportion, mean) - 1 Sampling...

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Sampling Distributions: The Fundamental Building Blocks of Statistical AnalysisSampling distributionsare probability distributions for estimators. Estimators are the sample statistics we use to make statements about population parameters. Population parameters are fixed and basically unknowable. They are not random variables. But the characteristics of sampling distributions (especially, unbiasedness and consistency) make it possible to make fairly specific statements about population parameters. These statements are probabilistic. (There is a probability the statement is true and a probability the statement is false.) This is the essence of statistical analysis.Take the sampling distribution of the proportion (nxp/) as an example. [This is fundamentally based on a binomial distribution (does the voter selected randomly from the population favor the candidate or not?), but we can invoke the central limit theorem, so the sampling distribution of the proportion is distributed normally for n30 or so.]))1(,(~nNpnpz)1(Say 45% of likely voters favor a candidate. Take a sample of 900 likely voters. If =.45 and n=900, what is the probability your sample proportion (p) of voters favoring the candidate would be .50 or greater? 1

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