Statistical Sciences 2244A/B Lecture Notes - Lecture 8: Central Limit Theorem, Null Hypothesis, Statistical Parameter
13 Apr 2018
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Document Summary
Apply the normal approximation to binomial distributions only when conducting inference. Central limit theorem applies to sampling distributions of sample means. Common statistic when dealing with categorical data. The mean of the sampling distribution is p. The standard deviation of the sampling distribution is sq(p(1-p)/n) As n increases, the sampling distribution of p hat becomes approximately normal. P hat is an unbiased estimator of p. The mean of the sampling distribution is the true value of the population proportion p. Standard deviation of p hat gets smaller as n increases. Normal approximation for the sampling distributions of p hat is least accurate when p is close to 0 or 1. Standard deviation of p hat is sq(p(1-p)/n) To estimate a population proportion p, use the sample proportion p hat level c con dence interval for p: p hat +- z*sq(p(1-p)/n) standard error of p hat: sq(p hat(1-p hat)/n)
