1. What is the Margin of Error?

The margin of error (MOE) is a statistic expressing the amount of random sampling error in a survey's results. It represents the radius of the confidence interval for a given statistic (usually a proportion) and indicates how close the sample statistic is likely to be to the true population parameter.

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 accounts for the variability in the sample proportion and the desired confidence level through the z-score.

3. Importance of Margin of Error

Details: The margin of error is crucial in survey research as it provides a range within which the true population parameter is likely to fall. A smaller margin of error indicates greater precision in the estimate.

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 (as a decimal between 0 and 1), and the sample size (must be a positive integer).

5. Frequently Asked Questions (FAQ)

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

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

Q3: How does sample size affect margin of error?
A: Margin of error decreases as sample size increases, following a square root relationship.

Q4: When is this formula appropriate?
A: For simple random sampling with replacement, or when sampling without replacement from a large population.

Q5: What's the relationship between MOE and confidence interval?
A: The confidence interval is calculated as [p - MOE, p + MOE] where p is the sample proportion.