A Margin of Error Calculator is a valuable statistical tool used to compute the accuracy of survey results or sample data.
It helps researchers and analysts estimate the range within which the true population parameter is likely to fall. This calculator takes into account factors such as sample size, confidence level, and population proportion to compute the margin of error.
Margin of Error Example Chart
| Sample Size | Confidence Level | Population Proportion | Margin of Error |
|---|---|---|---|
| 500 | 95% | 50% | 4.38% |
| 1000 | 99% | 30% | 3.79% |
| 2000 | 90% | 75% | 1.67% |
| 750 | 95% | 40% | 3.51% |
| 1500 | 99% | 60% | 3.31% |
Margin of Error Formula
The Margin of Error (MOE) formula is:
MOE = z √[(p (1-p)) / n]Where:
- z is the z-score based on the confidence level
- p is the population proportion
- n is the sample size
Let’s calculate the margin of error for a sample size of 1000, with a 95% confidence level and a population proportion of 50%.
- For a 95% confidence level, z = 1.96
- p = 0.5 (50%)
- n = 1000
MOE = 1.96 √[(0.5 (1-0.5)) / 1000]
= 1.96 * √(0.25 / 1000)
= 1.96 * √0.00025
= 1.96 * 0.0158
= 0.031 or 3.1%Thus, the margin of error in this example is 3.1%.
What is the Margin of Error in a Survey of 930 Students?
To calculate the margin of error for this scenario:
Sample size (n) = 930
Population proportion (p) = 0.92 (92%)
Assuming a 95% confidence level, z = 1.96
Using the formula:
MOE = 1.96 √[(0.92 (1-0.92)) / 930]
= 1.96 * √(0.0736 / 930)
= 1.96 * √0.0000791
= 1.96 * 0.00889
= 0.0174 or 1.74%The margin of error in this survey is approximately 1.74%.