Margin of Error

In the example of a survey for the legal protection of rainforests, 85% of the people responded positively.

This sample proportion could be different from the true population proportion due to the random variation in the population.

One can quantify this difference at a specific confidence level to understand how far the sample proportion from the true population proportion is.

The magnitude of this difference is called the margin of error, denoted as E.

It can be calculated by multiplying the critical value and the standard error of sample proportion using the following equation.

Here, z_⍺/2 is the critical value, is the sample proportion, is 1−, and n is the sample size.

So, in this example, where the sample proportion is 0.85, and the sample size is the total number of respondents—that is—10,000, at a 95% confidence level, the margin of error is 0.007.

So, the confidence interval can be expressed as 0.85±0.007, where the lower confidence limit is 0.843, and the upper limit is 0.857.