Point estimation

# Point estimation - Point Estimation of Means Point estimate...

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Point Estimation of Means Point estimate: x estimates μ Sample mean True but unknown population mean Questions: 1. How much information used in x ? 2. Possible size of the error in the estimation? Here “error” is error = “Sampling Error” = μ - x Because of luck, either good or bad, must always expect some error. Chance fluctuations of mean (and its reliability as an estimate of μ ) depends on: 1. the size n of the sample 2. the size of the population standard deviation σ (use s if σ is unknown or unavailable) Properties: 1. Unbiasedness: average of all possible point estimates is equal to the population parameter. For the mean: ( 29 μ = x E so x is an unbiased estimator of μ. The population variance σ 2 is defined as the average of squared deviation about the population mean μ, viz ( 29 2 1 2 1 = - = N i i x N μ σ The sample variance s 2 is defined as © 2000 by Harvey A. Singer 1

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( 29 2 1 2 1 1 = - - = n i i x x n s The sample variance is NOT strictly the average of the squared deviations around the sample mean x .
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