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Lecture9additional - Statistics 511 Statistical Methods Dr...

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Lecture 12: Some general concepts of point estimation Devore: Section 6.1 October, 2011 Page 1
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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Point estimator and a point estimate Let us denote an arbitrary parameter θ. It can be, for example, the population mean μ or the population variance σ 2 . Our purpose is to find a function of data that can provide a reasonable estimate of θ ; we denote such a function ˆ θ and call it a point estimator As an example, let θ be μ. Given sample X 1 , . . . , X n we can estimate μ as ¯ X. The statistic ¯ X is called a point estimator of the mean μ ; to stress the fact that its purpose is to estimate μ we denote it ˆ μ A particular value of ˆ μ for a given sample is called a point estimate October, 2011 Page 2
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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Example I Let X the number of crashes of cars with the new bumper type that result in no visible damage; the total number of tests is n The estimator of the true proportion of successful outcomes p is ˆ p = X n If n = 25 and X = 15 for a given sample of n tests, the estimate is 15 25 = 0 . 6 October, 2011 Page 3
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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Example II
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