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Unformatted text preview: 5.1 The Sampling Distribution of a Sample Mean (old 5.2) •averages are less variable than individual observations •averages are more normal than individual observations The mean and standard deviation of x x = mean of sample, μ = mean of population, σ 2 = population variance select an SRS of size n from a population and measure variable X on each individual in sample the n measurements are values of n random variables- X 1 , X 2 … X n • X i is measurement on one individual selected at random from population→ then X i has the distribution of the population •if population is large relative to the size of the sample→ X 1 , X 2 … X n considered independent Mean and standard deviation of a sample mean Let x be the mean of an SRS of size n from a population having mean μ and standard deviation σ. The mean and standard deviation of x are: x μ = μ x σ = n σ ●increasing sample size reduces sampling variability Sampling distribution of a sample mean If a population has the N(μ, σ ) distribution, then the sample mean x of n independent observations has the N(μ, n σ ) distribution....
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This note was uploaded on 02/22/2012 for the course PAM 2100 taught by Professor Abdus,s. during the Fall '08 term at Cornell.
- Fall '08