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 reported percentage 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 (based on confidence level)
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula calculates the range within which the true population parameter is expected to fall with a given level of confidence.

3. Importance of Margin of Error Calculation

Details: Margin of Error is crucial for understanding the precision of survey results and making informed decisions based on statistical data. It helps determine how much confidence we can have in survey findings.

4. Using the Calculator

Tips: Enter the z-score (typically 1.96 for 95% confidence), sample proportion (between 0-1), and sample size. All values must be valid (n > 0, 0 ≤ p ≤ 1).

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 margin of error?
A: Larger sample sizes result in smaller margins of error, providing more precise estimates.

Q3: When should I use 0.5 for proportion?
A: Use p=0.5 when you want the maximum margin of error or when the true proportion is unknown, as it gives the most conservative estimate.

Q4: What's the relationship between confidence level and margin of error?
A: Higher confidence levels result in larger margins of error, as they require wider intervals to be more certain of capturing the true parameter.

Q5: Can margin of error be negative?
A: No, margin of error is always a positive value representing the plus/minus range around the sample statistic.