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Unformatted text preview: Statistics 528  Lecture 20 1 Statistics 528  Lecture 20 Prof. Kate Calder 1 The Sampling Distribution of the Sample Mean • Imagine that we have an SRS of size n from a population and measure a variable X on each individual in the sample. • Each X i is a measurement from the population and therefore has the distribution of the population => & Xi = & and ¡ Xi = ¡ . • The sample mean of an SRS of size n is ) ( 1 2 1 n X X X n x + + + = & Statistics 528  Lecture 20 Prof. Kate Calder 2 Question: What are the mean and standard deviation of ? The mean of distribution of the sample mean: => is an unbiased estimate of & . x ) ( 1 2 1 n x x x x n μ μ μ μ + + + = & ) ( 1 μ μ μ + + + = & n μ = x Statistics 528  Lecture 20 2 Statistics 528  Lecture 20 Prof. Kate Calder 3 The standard deviation of distribution of the sample mean: The observations are independent, so we can use addition rule for variances  So, ) ( 1 2 2 2 2 2 2 1 n x x x x n σ σ σ σ + + + & ¡ ¢...
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This note was uploaded on 07/26/2011 for the course STA 528 taught by Professor Calder during the Winter '09 term at Ohio State.
 Winter '09
 Calder

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