1. What is Margin of Error?

The margin of error (MOE) represents the range of values above and below the sample statistic in a confidence interval. It quantifies the uncertainty in estimating a population parameter from sample data.

2. How Does the Calculator Work?

The calculator uses the margin of error formula:

Where:

• \( z \) — Z-score (standard score)
• \( SD \) — Standard deviation of the population
• \( n \) — Sample size

Explanation: The margin of error increases with higher confidence levels (larger z-scores) and population variability (larger SD), but decreases with larger sample sizes.

3. Importance of Margin of Error

Details: Margin of error is crucial in survey research and statistical analysis as it provides a measure of the precision of sample estimates and helps determine appropriate sample sizes for desired confidence levels.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: How does sample size affect MOE?
A: MOE decreases as sample size increases, but with diminishing returns (halving MOE requires quadrupling sample size).

Q3: What if I don't know the population SD?
A: Use the sample standard deviation as an estimate when population SD is unknown.

Q4: How is MOE related to confidence intervals?
A: The confidence interval is calculated as [sample mean - MOE, sample mean + MOE].

Q5: When should I use this formula?
A: For normally distributed data when estimating means with known population standard deviation (z-test conditions).