lecture 10 Sampling distribution

# lecture 10 Sampling distribution - Sampling Distribution...

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Sampling Distribution The distribution of a given sample statistic for all possible samples of a given size taken from a population Sampling Distribution of the Mean Mean of all Sample Means: E(X) = μ Variance of all Sample Means: Var(X) = ? 1

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Variance of the Mean Var(X) = Var( x i /n) [Var( x i )]/n 2 [n · Var(X)]/n 2 σ 2 /n As the sample size, n , increases, the variance of the sampling distribution of the mean, Var(X) = σ 2 /n , decreases 2
Variance of the Mean (x - c) 2 /n = (x - X + X - c) 2 /n ((x - X) + (X - c)) 2 /n [ (x - X) 2 + 2 (X - c) (x - X) + n(X - c) 2 ]/n (x - c) 2 /n = (x - X) 2 /n + (X - c) 2 (x - μ) 2 /n = (x - X) 2 /n + (X - μ) 2 3

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Variance of the Mean and Degrees of Freedom (x - μ) 2 /n = (x - X) 2 /n + (X - μ) 2 σ 2 = (x - X) 2 /n + σ 2 /n n σ 2 - σ 2 = (x - X) 2 σ 2 (n - 1) = (x - X) 2 σ 2 = (x - X) 2 /(n - 1) = s 2 ^ ^ ^ ^ ^ ^ 4
Central Limit Theorem When the sample size is large enough the sampling

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## This note was uploaded on 01/21/2009 for the course PSYC 60 taught by Professor Ard during the Winter '08 term at UCSD.

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lecture 10 Sampling distribution - Sampling Distribution...

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