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 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 (critical value for desired confidence level)
• \( sd \) — Standard deviation of the population
• \( n \) — Sample size

Explanation: The formula shows that margin of error decreases as sample size increases, and increases with greater variability in the population.

3. Importance of Margin of Error

Details: Margin of error is crucial in survey research and statistical analysis 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 (1.96 for 95% confidence), standard deviation, and sample size. All values must be valid (n > 0, sd ≥ 0).

5. Frequently Asked Questions (FAQ)

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

Q2: What if I don't know the population standard deviation?
A: You can use the sample standard deviation as an estimate, or use 0.5 for maximum variability (conservative estimate).

Q3: How does sample size affect margin of error?
A: MOE decreases as sample size increases, but the relationship is not linear - doubling sample size reduces MOE by about 1/√2.

Q4: What's a good margin of error?
A: This depends on context. For political polling, 3-5% is typical. For scientific research, smaller margins are preferred.

Q5: Can margin of error be zero?
A: Only with a census (entire population surveyed) or if there's no variability in responses (sd=0).