# Interpret the margin of error for Sample Size for Estimation

The margin of error quantifies the amount of random sampling error in the estimation of a parameter, such as the mean or proportion. A margin of error is often used in survey results. For example, a political poll might report that a candidate's approval rating is 55%, with a 5% margin of error. This means that the true approval rating is +/– 5%, and is somewhere between 50% and 60%.

## Interpretation

For a two-sided confidence interval, the margin of error is the distance from the estimated statistic to each end point. When a confidence interval is symmetric, the margin of error is half the width of the confidence interval. For example, if the mean estimated length of a camshaft is 600 mm and the confidence interval is 599 to 601, then the margin of error is 1 mm. When the confidence interval is not symmetric, Minitab displays two values that represent the distance from the estimated statistic to each end point.

The greater the margin of error is, the wider the interval is, and the less precise the parameter estimate.

For a binomial distribution, the margin of error is greatest when the planning proportion is 0.50. When the sample proportion is further from 0.50 than the planning proportion, the margins of error for the sample are smaller than the planning margins of error.

In the following results, a hospital researcher wants to determine the margin of error associated with a 95% confidence interval for the proportion of patient records that contains missing information based on a sample size of 80. Based on this sample size and a planning value proportion of 0.2, the margin of error in the direction of the lower bound is approximately 0.081. The margin of error in the direction of the upper bound is approximately 0.104. If the researcher's sample proportion is 0.2 for a sample size of 80, then the confidence interval will be (0.20 – 0.081, 0.20 + 0.104).

## Method

 Proportion Binomial 0.2 95% Two-sided

## Results

Sample SizeMargin of Error
(Lower Bound)
Margin of Error
(Upper Bound)
800.08114090.104369