1. What is Margin of Error?

The margin of error (MOE) quantifies the amount of random sampling error in a survey's results. It represents the radius of the confidence interval for a given statistic. At 95% confidence level, there's a 95% probability that the true population parameter lies within the margin of error of the sample statistic.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size
• 1.96 — Z-score for 95% confidence level

Explanation: The formula accounts for both the sample proportion and sample size to estimate the precision of the survey results.

3. Importance of Margin of Error

Details: Understanding MOE is crucial for interpreting survey results, determining required sample sizes, and assessing the reliability of statistical estimates.

4. Using the Calculator

Tips: Enter the sample proportion (as a decimal between 0 and 1) and the sample size. Both values must be valid (0 ≤ p ≤ 1, n > 0).

5. Frequently Asked Questions (FAQ)

Q1: Why 1.96 in the formula?
A: 1.96 is the z-score that corresponds to 95% confidence level in a normal distribution.

Q2: What if I don't know the exact proportion?
A: Use p = 0.5 for maximum margin of error (most conservative estimate).

Q3: How does sample size affect MOE?
A: MOE decreases as sample size increases, following an inverse square root relationship.

Q4: Can I use this for non-binary variables?
A: This formula is for proportions. For continuous variables, different formulas apply.

Q5: What confidence level does this use?
A: This calculator uses 95% confidence level. For other levels, the z-score would change.