Ch 7 Sec 1

Ch 7 Sec 1 - Chapter 7 Section 1 1 Confidence Intervals and...

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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 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 . 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 . 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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Ch 7 Sec 1 - Chapter 7 Section 1 1 Confidence Intervals and...

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