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.

2. How Does the Calculator Work?

The calculator uses the margin of error formula:

Where:

• \( z \) — Z-score (critical value)
• \( SD \) — Standard deviation
• \( n \) — Sample size

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

3. Importance of Margin of Error

Details: The margin of error is crucial in determining the precision of survey results and constructing confidence intervals. It helps researchers understand the reliability of their data.

4. Using the Calculator

Tips: Enter the z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the standard deviation of your data, and the sample size.

5. Frequently Asked Questions (FAQ)

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

Q2: How does sample size affect MOE?
A: MOE decreases as sample size increases, following a square root relationship (doubling sample size reduces MOE by √2 ≈ 1.41).

Q3: What if I don't know the standard deviation?
A: For proportions, use SD = √(p(1-p)) where p is the sample proportion. For unknown SD in small samples, use t-scores instead.

Q4: When is this formula not appropriate?
A: For small samples (n < 30) from non-normal populations, or when sampling without replacement from small populations.

Q5: How is MOE related to confidence intervals?
A: The confidence interval is calculated as [point estimate - MOE, point estimate + MOE].