1. What is 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.

2. How Does the Calculator Work?

The calculator uses the margin of error formula:

Where:

• \( z \) — Z-score (critical value for desired confidence level)
• \( SD \) — Standard deviation of the population
• \( n \) — Sample size

Explanation: The margin of error increases with higher standard deviation and decreases with larger sample sizes. Common z-scores are 1.96 (95% confidence) and 2.576 (99% confidence).

3. Importance of Margin of Error

Details: Margin of error is crucial in survey sampling and experimental design as it quantifies the uncertainty in estimates. It helps determine how much survey results might differ from the true population value.

4. Using the Calculator

Tips: Enter the z-score appropriate for your desired confidence level, the standard deviation of your data, and your sample size. All values must be valid (n > 0, SD ≥ 0).

5. Frequently Asked Questions (FAQ)

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

Q2: How does sample size affect margin of error?
A: Margin of error decreases as sample size increases, but the relationship is not linear (halving MOE requires quadrupling sample size).

Q3: When should I use this formula?
A: When you know the population standard deviation and are working with a normally distributed sampling distribution.

Q4: What if I don't know the population standard deviation?
A: For small samples (n < 30), use the t-distribution instead of the z-score.

Q5: How accurate is this calculation?
A: The formula provides the theoretical margin of error assuming random sampling and normal distribution. Real-world factors may affect actual error.