In the popular media, the margin of error is the most frequently quoted measure of statistical accuracy for a sample estimate of a population parameter. Based on the conventional definition of the measure, the difference between the estimate and the targeted parameter should be bounded by the margin of error 95% of the time. Thus, only 1 in 20 surveys or studies should lead to a result in which the actual estimation error exceeds the margin of error.

Technically, the margin of error is defined as the radius or the half-width of a symmetric confidence interval. To formalize this definition, suppose that the targeted population parameter is denoted by θ. Let θ represent an estimator of θ based on the sample data. Let SDθ denote the ...

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