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Unformatted text preview: Chapter 7 Section 1 1 Confidence Intervals and Sample Size Mr. Kenneth Horwitz November 10, 2010 Confidence Intervals for the Mean When s Is Known and Sample Size A point estimate is a specific numerical value estimate of a parameter. The best point estimate of the population mean µ is the sample mean 2 . X Finding a point estimate Market researchers use the number of sentences per advertisement as a measure of readability for magazine advertisements. The following represents a random sample of the number of sentences found in 50 advertisements. Find a point estimate of the population mean µ. 9, 20, 18, 16, 9, 9, 11, 13, 22, 16, 5, 18, 6, 6, 5, 12, 25 17, 23, 7, 10, 9, 10, 10, 5, 11, 18, 9, 9, 17, 13, 11, 7, 14, 6, 11, 12, 11, 6, 12, 14, 11, 9, 18, 12, 12, 17, 11, 20 3 Finding a point estimate Step 1 – Find the sample mean. Since we have already learned that the mean of all sample means equals the population mean. As a result is an unbiased estimator of µ. So your point estimate for the mean length of all magazine advertisements is 12.04 sentences. 4 12.04 X = X Three Properties of a Good Estimator 1. The estimator should be an unbiased estimator . That is, the expected value or the mean of the estimates obtained from samples of a given size is equal to the parameter being estimated. 5 Three Properties of a Good Estimator 2. The estimator should be consistent. For a consistent estimator , as sample size increases, the value of the estimator approaches the value of the parameter estimated. 6 Three Properties of a Good Estimator 3. The estimator should be a relatively efficient estimator ; that is, of all the statistics that can be used to estimate a parameter, the relatively efficient estimator has the smallest variance....
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 Fall '10
 Nielson
 Statistics

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