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Unformatted text preview: Revised on 11/9/2011 19:08 a11/p11 Chapter 5 Statistical Inference Methods of Statistical Inference: • Point Estimation • Interval Estimation • Significance Tests (Chapter 6) 5.1 Point Estimation A point estimator of a parameter is the sample statistic that predicts the value of the parameter. • A point estimator of the population mean is the sample mean: X ˆ X μ = • A point estimator of the population variance is the sample variance: 2 2 X X ˆ S σ = • A point estimator of the population proportion is the sample proportion ˆ p π = Desirable properties of Point Estimators: • Efficiency • Unbiasedness • Normality The above estimators have the following properties: 1. They are efficient , i.e. one cannot find other estimators that have smaller standard errors and these estimators are closer to the true parameter values. 2. They are unbiased . In repeated sampling the estimates average out to give the true values of the parameters. (S is not an unbiased estimator of σ but its bias is small and decreases as the sample size increases.) 3. The sample mean and the sample proportion have approximate normal distributions (but not the sample variance). General formula for a confidence interval CI = (Estimate ± Margin of Error) ME = Margin of Error = (table value) × (Standard Error of Estimate) The width of a CI • Increases as the confidence level increases • Decreases as the sample size increases. STA6126 Chapter 5,Page 1 of 4 5.2 CI for population proportion π : Using the general formula we may also write An approximate confidence interval for π is ( 29 p ME ± and 1 p( p ) ME z n - = × ÷ ÷ When np ≥ 15 and n(1 – p) ≥ 15 5.3 Confidence interval for the mean 5....
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