1. What is the 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 corresponding to the desired confidence level
• \( SD \) — Standard deviation of the population
• \( n \) — Sample size

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

3. Importance of Margin of Error

Details: The margin of error is crucial in statistical analysis as it provides a range within which the true population parameter is likely to fall. It helps assess the reliability of survey results and experimental findings.

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 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 MOE?
A: MOE decreases as sample size increases, following an inverse square root relationship.

Q3: When should I use this formula?
A: Use it when estimating the mean of a normally distributed population with known standard deviation.

Q4: What if population SD is unknown?
A: For large samples (n > 30), you can use sample standard deviation. For small samples, use t-distribution instead.

Q5: How to interpret MOE?
A: If your sample mean is x with MOE m, you can be confident that the population mean is between x-m and x+m.