1. What is the Margin of Error Formula?

The Margin of Error (MOE) formula calculates the range of uncertainty around a sample statistic. It's commonly used in survey results to indicate how much the sample results might differ from the true population value.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

• \( z \) — Z-score (standard score indicating confidence level)
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula accounts for the relationship between sample size, proportion, and desired confidence level to estimate the potential error in survey results.

3. Importance of Margin of Error

Details: Margin of Error is crucial for understanding the reliability of survey results and making informed decisions based on sample data. A smaller MOE indicates more precise results.

4. Using the Calculator

Tips: Enter the z-score (common values: 1.96 for 95% CI, 2.576 for 99% CI), the sample proportion (0-1), and the sample size. All values must be valid (n > 0, 0 ≤ p ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is a good margin of error?
A: Typically, MOE ≤ 5% is considered acceptable for most surveys, but the appropriate level depends on your specific needs.

Q2: How does sample size affect MOE?
A: As sample size increases, MOE decreases. Doubling the sample size reduces MOE by about 30%.

Q3: What z-score should I use?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

Q4: What if I don't know the proportion?
A: Use p = 0.5 as it gives the maximum MOE (most conservative estimate).

Q5: Can MOE be greater than 100%?
A: Mathematically possible with very small samples, but practically MOE > 100% indicates the survey results are unreliable.