Sample size, the Margin of Error and the Coefficient of Variation

by Robert M. Lynch and Brian Kim

Abstract: In introductory statistics, students are taught to determine the sample size required for a specified Margin of Error (ME) with a known estimated standard deviation for a population. Students are frequently challenged to identify a ME associated with the mean. They are more comfortable with identifying a ME for a sample proportion and frequently respond with 3 percent or 4 percent as these are common values used by the pollsters in election coverage and other polls. Applying the same approach to mean estimation, students become comfortable with estimates that are within a specified percent of the mean. For example, if it is believed a population mean is near 500, a 3 percent margin of error suggests a ME equal to 15 units and a 4 percent ME suggests an error of 20 units. Once the ME is established, the sample size (N) that would yield such an error can be determined. A relationship exits between the ME when calculated as a percent of the mean, the Coefficient of Variation (CV) and the sample size. This paper describes the relationship, provides the algebraic equivalencies to the common sample size formula and presents several illustrations. It also identifies several findings.

Key Words: size, Margin of Error, Coefficient of Variation

Authors:
Robert Lynch, , robert.lynch@unco.edu
Brian Kim, mkim2@ilstu.edu

Editor: Graf, R.G. ,rgraf@sunstroke.sdsu.edu

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