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Politics : PRESIDENT GEORGE W. BUSH
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To: nihil who wrote (37012)9/15/2000 7:52:12 AM
From: Neocon  Read Replies (1) of 769667
 
statistics

Estimation of a population mean

When the sample mean is used as a point estimate of the population mean, some error can be expected owing to the fact that a sample, or subset of the population, is used to compute the point estimate....The standard deviation of a sampling distribution is called the standard error....
In the large-sample case, a 95% confidence interval estimate for the population mean is given by +/- 1.96/n, (where n equals the sample size).....The quantity 1.96/n is often called the margin of error for the estimate. ....The interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean. Thus, any interval computed in this manner has a 95% confidence of containing the population mean. By changing the constant from 1.96 to 1.645, a 90% confidence interval can be obtained. It should be noted from the formula for an interval estimate that a 90% confidence interval is narrower than a 95% confidence interval and as such has a slightly smaller confidence of including the population mean. Lower levels of confidence lead to even more narrow intervals. In practice, a 95% confidence interval is the most widely used.

....the sample size affects the margin of error. Larger sample sizes lead to smaller margins of error. This observation forms the basis for procedures used to select the sample size. Sample sizes can be chosen such that the confidence interval satisfies any desired requirements about the size of the margin of error.

britannica.com
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