Enter the confidence level, sample size, and population proportion into the calculator to determine the margin of error for a survey or experiment.
Margin of Error Formula
The following formula is used to calculate the margin of error.
MOE = Z * sqrt((P * (1 - P)) / n)
Variables:
- MOE is the margin of error
- Z is the z-score corresponding to the desired confidence level
- P is the population proportion (expressed as a decimal)
- n is the sample size
To calculate the margin of error, multiply the z-score corresponding to the desired confidence level by the square root of the population proportion times one minus the population proportion divided by the sample size.
What is Margin of Error?
The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. It represents the range within which we can expect the true value to lie with a certain level of confidence. The margin of error increases with the level of confidence but decreases with the sample size and the population proportion. It is a crucial concept in statistics and is used to express the precision of an estimate.
How to Calculate Margin of Error?
The following steps outline how to calculate the Margin of Error.
- First, determine the confidence level and find the corresponding z-score.
- Next, determine the sample size (n).
- Next, determine the population proportion (P) as a decimal.
- Next, gather the formula from above = MOE = Z * sqrt((P * (1 – P)) / n).
- Finally, calculate the Margin of Error (MOE).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Confidence Level = 95%
Sample Size (n) = 1000
Population Proportion (P) = 0.5
