1. What is a Margin of Error Calculator?

Definition: This calculator estimates the margin of error for a given confidence level, proportion, and sample size in statistical sampling.

Purpose: It helps researchers, survey analysts, and statisticians determine the precision of their sample estimates.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( E \) — Margin of error
• \( Z \) — Z-score (critical value for confidence level)
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula calculates the radius of the confidence interval for a population proportion.

3. Importance of Margin of Error Calculation

Details: Understanding the margin of error is crucial for interpreting survey results and determining the reliability of statistical estimates.

4. Using the Calculator

Tips: Enter the Z-score (1.96 for 95% confidence), proportion (default 0.5 for maximum variability), and sample size. All values must be valid (0 ≤ p ≤ 1, n > 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common values are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: Why use p=0.5 as default?
A: p=0.5 gives the maximum margin of error, providing the most conservative estimate when the true proportion is unknown.

Q3: How does sample size affect the margin of error?
A: Margin of error decreases as sample size increases, but the relationship is not linear (doubling sample size doesn't halve the margin).

Q4: Can I use this for continuous data?
A: This formula is for proportions. For means, use \( E = Z \times \frac{\sigma}{\sqrt{n}} \) where σ is the standard deviation.

Q5: What's a good margin of error?
A: Typically 3-5% for political polls, but depends on your research needs. Smaller margins require larger samples.