Margin of Error

The term margin of error is most commonly used in the scientific literature to describe how close a sample statistic, $\widehat{\mathrm{\theta }},$ is to an unknown population parameter, θ. Assuming the sampling distribution of $\widehat{\mathrm{\theta }}$ is approximately symmetric, a confidence interval for θ will be

$$\widehat{\mathrm{\theta }}\pm m,$$

where m is the margin of error. The margin of error in confidence intervals such as these is made up of two components: the confidence level of the interval and the standard deviation or standard error of the statistic estimating the unknown parameter θ. For example, suppose one is estimating the level of support for a public proposition, such as the legalization of marijuana. If sample ...