Point Estimation

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• Point Estimation

• Estimatior - any statistic to estimate a characteristic of a population

• Unbiased estimator is denoted by: E(T)=α

• The most efficient and best estimator for α, is the estimator that:is unbiasedhas the smallest variance

• Most Efficient of Population Mean

• Unbiased Estimator:

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• Most Efficient of Population Variance

• Best unbiased estimator of population variance: σ̂^2S^2 = variance of the sample

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• Can also be noted as

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• Best Unbiased Estimator of a Probability/Proportion

• X~Bin(n,α)unbiased estimator:          Estimated Standard Error:                           p̂=Ps where Ps = sample proportion

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• Distribution of the Sample Proportion

• For both np>5 and nq>5 a continuity correction needs to be used.If n>30, by C.L.T. :-                      Continuity correction for                  is:             if using equation above

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