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Stats 309 10-1 to 10-2

Stats 309 10-1 to 10-2 - 10.1 Estimation Objective of...

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10.1 Estimation Objective of estimation is to determine the approximate value of a population parameter. We can calculate a sample mean and use that to estimate the value of the population parameter. When we do that, it is called the point estimator . A point estimator draws inferences about a population by estimating the value of an unknown parameter using a single value or point. However, we know that the sample mean is probably not exactly the same as the population parameter. So instead, we calculate an interval around the sample mean, and we can say with confidence that this interval traps the population parameter. This is an interval estimator . An interval estimator draws inferences about a population by estimating the value of an unknown parameter using an interval. An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter. Like E(x-bar) = µ so x-bar is an unbiased estimator of µ. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. So, x-bar is a consistent estimator of μ because the variance of x-bar is σ 2 /n.

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