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Unformatted text preview: Apr 7’10 STATISTICAL ESTIMATION. CONFIDENCE INTERVAL #10 FOR A POPULATION MEAN. THE t DISTRIBUTION. By definition , statistical inference is a procedure by which we reach a conclusion about a population on the basis of the information contained in a sample drawn from that population . Estimation is the first of the two general areas of statistical inference. (The second general area is hypothesis testing .) There is no any single universal computational techniques for statistical inference; we’ll learn different techniques each for certain conditions of application. The process of estimation assumes calculating, from the data of a sample , some statistic that is offered as an approximation of the corresponding parameter of the population from which the sample was drawn. Many populations of interest, also finite, are so large that a 100% examination would be prohibitive from the standpoint of cost, and we have to rely on the estimations of statistical parameters obtained for the samples of smaller size. For each of the statistical parameters we can compute two types of estimate: a point estimate and an interval estimate. By definition , a point estimate is a single numerical value used to estimate the corresponding population parameter. An interval estimate consists of two numerical values defining a range of values that, with a specific degree of confidence, we feel includes the parameter being estimated. An estimate and an estimator . Note that a single computed value has been referred to as an estimate . The rule that tells us how to compute this value, or estimate, is referred to as an estimator. _ Estimators are usually presented as formulas. For example, a sample mean x = Σ x i /n is an estimator for the population mean µ (though a sample median also could be used to estimate µ ). When a parameter may be estimated by more than one estimator we need in criteria that allow us to choose the best one. The property of unbiasness is one of these criteria. Definitions . The sampled population is the population from which one actually draws a sample. The target population is the population about which one wishes to make an inference. These two populations may or may not be the same. Proper statistical inference procedures allow one to make inferences about sampled populations. If the sampled population and the target population are different, the researcher can reach conclusions about the target population only on the basis of nonstatistical considerations. The strict validity of the statistical procedures depends on the assumption that the data used for analysis have come from randomly selected samples. In real-world applications it is impossible or impractical to use truly random samples. Researches have to involve nonstatistical considerations to prove that actually used samples are equivalent to simple random samples....
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- Spring '05
- Normal Distribution