7.7:
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.
7.7:
Margin of Error
The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic. The margin of error is calculated at a pre-decided significance level, most commonly at 95%.
For the population parameters such as proportion, mean, or variance, the margin of error (denoted as E) is calculated differently. For the proportion, it utilizes the point estimate of proportion (sample proportion) and the sample size.
The margin of error also indicates the amount or magnitude of random sampling error in the sampling effort, the study, or the survey results. However, it should not be confused with the Type-I and Type-II errors. The margin of error is also NOT a measure of any sampling bias, measurement error, calculation error, experimental design error, or errors in the sampling or experimental methods followed during the study. E helps generate the appropriate confidence limits in estimating the population parameter. E is essential as the confidence limits are calculated using the E.