Eco 3411 47 properties of point estimators efficiency

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Unformatted text preview: area = (.2291)(2) = .4582. The probability is .4582 that the sample proportion will be ECO 3411 45 within +/-.05 of the actual population proportion. Properties of Point Estimators • Before using a sample statistic as a point estimator, statisticians check to see whether the sample statistic has the following properties associated with good point estimators. – Unbiasedness – Efficiency – Consistency ECO 3411 46 Properties of Point Estimators • Unbiasedness If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to be an unbiased estimator of the population parameter. ECO 3411 47 Properties of Point Estimators • Efficiency Given the choice of two unbiased estimators of the same population parameter, we would prefer to use the point estimator with the smaller standard deviation, since it tends to provide estimates closer to the population parameter. The point estimator with the smaller standard deviation is said to have greater relative efficiency than the other. ECO 3411 48 Properties of Point Estimators • Consistency A point estimator is consistent if the values of the point estimator tend to become closer to the population parameter as the sample size becomes larger. ECO 3411 49 Other Sampling Methods • • • • Stratified Random Sampling Cluster Sampling Systematic Sampling Convenience Sampling ECO 3411 50 Stratified Random Sampling The population is first divided into groups of The population is first divided into groups of elements called strata.. elements called strata Each element in the population belongs to one and Each element in the population belongs to one and only one stratum. only one stratum. Best results are obtained when the elements within Best results are obtained when the elements within each stratum are as much alike as possible each stratum are as much alike as possible (i.e. a homogeneous group). (i.e. a homogeneous group). ECO 3411 51 Stratified Random Sampling A simple random sample is taken from each stratum. A simple random sample is taken from...
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