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Introduction to Estimation.doc

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Stats: Introduction to Estimation -------------------------------------------------------------------------------- One area of concern in inferential statistics is the estimation of the population parameter from the sample statistic. It is important to realize the order here. The sample statistic is calculated from the sample data and the population parameter is inferred (or estimated) from this sample statistic. Let me say that again: Statistics are calculated, parameters are estimated. We talked about problems of obtaining the value of the parameter earlier in the course when we talked about sampling techniques. Another area of inferential statistics is sample size determination. That is, how large of a sample should be taken to make an accurate estimation. In these cases, the statistics can't be used since the sample hasn't been taken yet. Point Estimates There are two types of estimates we will find: Point Estimates and Interval Estimates. The point estimate is the single best value. A good estimator must satisfy three conditions: •Unbiased: The expected value of the estimator must be equal to the mean of the parameter •Consistent: The value of the estimator approaches the value of the parameter as the sample size increases •Relatively Efficient: The estimator has the smallest variance of all estimators which could be used Confidence Intervals The point estimate is going to be different from the population parameter because due to the sampling error, and there is no way to know who close it is to the actual parameter. For this reason, statisticians like to give an interval estimate which is a range of values used to estimate the parameter. A confidence interval is an interval estimate with a specific level of confidence. A level of confidence is the probability that the interval estimate will contain the parameter. The level of confidence is 1 - alpha. 1-alpha area lies within the confidence interval. Maximum Error of the Estimate The maxim
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