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.

2. How Does the Calculator Work?

The calculator uses the margin of error formula:

Where:

• \( z \) — Z-score (standard score)
• \( p \) — Sample proportion
• \( n \) — Sample size

Explanation: The formula calculates how much the sample results may differ from the true population value.

3. Importance of Margin of Error

Details: Margin of error is crucial in determining the reliability of survey results. A smaller MOE indicates more confidence in the results being close to the true population value.

4. Using the Calculator

Tips: Enter the z-score (common values: 1.96 for 95% confidence, 2.58 for 99% confidence), sample proportion (between 0 and 1), and sample size (positive integer).

5. Frequently Asked Questions (FAQ)

Q1: What is a good margin of error?
A: Typically, a margin of error of 5% or less is considered acceptable for most surveys, though this depends on the specific research context.

Q2: How does sample size affect margin of error?
A: As sample size increases, margin of error decreases. The relationship is inverse square root - to halve the MOE, you need to quadruple the sample size.

Q3: What z-score should I use?
A: Common z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q4: What if my proportion is unknown?
A: Use p = 0.5 as this gives the maximum margin of error (most conservative estimate).

Q5: Can this be used for continuous data?
A: For means, the formula is different: \( MOE = z \times \frac{\sigma}{\sqrt{n}} \), where σ is the standard deviation.