How To Calculate Margin Of Error For One Sample Proportion

Calculating the margin of error (MOE) for a single sample proportion is crucial in statistics to determine the reliability of your estimates. It helps you understand the precision of your sample data and how well it represents the entire population.

1. Enter the sample size.
2. Enter the proportion (between 0 and 1).
3. Select the desired confidence level.
4. Click “Calculate”.

The formula to calculate the margin of error for one sample proportion is:

MOE = Z * sqrt[(P * (1 - P)) / n]

Where:

• Z is the Z-score based on the chosen confidence level.
• P is the sample proportion.
• n is the sample size.

Examples

Suppose you conduct a survey of 100 people and find that 60 of them support a new policy. With a 95% confidence level, the margin of error is:

MOE = 1.96 * sqrt[(0.6 * (1 - 0.6)) / 100] ≈ 0.077

So, you can be 95% confident that the true support for the policy is between 52.3% and 67.7%.

Comparison Tables

Sample Size	Proportion	90% MOE	95% MOE	99% MOE
50	0.5	0.14	0.16	0.21
100	0.5	0.10	0.11	0.15

Expert Tips

• Larger sample sizes result in smaller margins of error.
• A higher confidence level results in a larger margin of error.
• If your sample proportion is close to 0 or 1, the margin of error will be larger.

FAQ

What is a Z-score?

A Z-score is a statistical measure that indicates how many standard deviations an element is from the mean.

U.S. Census Bureau – Margin of Error

Statistics How To – Margin of Error Formula