1. What is the Margin of Error?

The Margin of Error (MOE) represents the range of values above and below the sample proportion in a confidence interval. It quantifies the uncertainty in survey results and helps determine how closely the sample results reflect the true population values.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

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

Explanation: The formula calculates the margin of error as a percentage, accounting for sample size, proportion, and the desired confidence level through the z-score.

3. Importance of Margin of Error Calculation

Details: Calculating margin of error is essential for determining the reliability of survey results, establishing confidence intervals, and making informed decisions based on sample data with known precision.

4. Using the Calculator

Tips: Enter the z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the sample proportion (between 0 and 1), and the sample size. All values must be valid (n > 0, 0 ≤ p ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What are common z-score values?
A: Common z-scores: 1.645 (90% confidence), 1.96 (95% confidence), 2.576 (99% confidence).

Q2: How does sample size affect margin of error?
A: Larger sample sizes result in smaller margins of error, providing more precise estimates of population parameters.

Q3: What if I don't know the proportion?
A: When the proportion is unknown, use p = 0.5 as this maximizes the margin of error and provides the most conservative estimate.

Q4: Can margin of error be negative?
A: No, margin of error is always expressed as a positive percentage representing the range around the sample estimate.

Q5: How is margin of error used in reporting results?
A: Results are typically reported as "X% ± Y%" where Y is the margin of error, indicating the range within which the true population value likely falls.