CENTRAL LIMIT THEOREM: STATEMENT Consider a large population: Population mean= Y μ Population variance = Y 2 σ Take all possible samples of size n from this population and compute the sample means Y . The Central Limit Theorem states the following: 1. The mean of the sampling distribution of the mean is equal to the population mean (i.e. Y Y E = ) ( 2. The variance of the sampling distribution of the mean is equal to the population variance divided by the sample size (n) i.e. n Y Y / 2 2 = (Therefore the standard deviation (or standard error) of the mean is the population standard deviation divided by the square root of the number of observations i.e.
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