1. What is Margin of Error?

The Margin of Error (ME) 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 and indicates how close the sample results are likely to be to the true population value.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

• \( z \) — Z-score corresponding to the desired confidence level
• \( sd \) — Standard deviation of the sample
• \( n \) — Sample size

Explanation: The formula shows that margin of error decreases as sample size increases, and increases with higher standard deviation or higher confidence levels (larger z-scores).

3. Importance of Margin of Error

Details: Margin of Error is crucial in survey sampling as it provides a range within which the true population parameter is likely to fall. It helps assess the reliability and precision of survey results.

4. Using the Calculator

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

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

Q3: When is this formula appropriate?
A: When sampling from a normally distributed population or when sample size is large enough (n ≥ 30) for the Central Limit Theorem to apply.

Q4: What if I don't know the population standard deviation?
A: For large samples, you can use the sample standard deviation as an estimate.

Q5: How is this different from confidence interval?
A: Margin of error is half the width of the confidence interval. A 95% CI would be: estimate ± ME.