1. What is Sample Proportion Error?

The sample proportion error (margin of error) quantifies the uncertainty in estimating a population proportion from a sample. It provides a range within which the true population proportion is likely to fall.

2. How Does the Calculator Work?

The calculator uses the sample proportion error formula:

Where:

• \( z \) — Z-score corresponding to the desired confidence level
• \( \hat{p} \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula accounts for both the sample size and the variability in the proportion estimate, scaled by the confidence level (z-score).

3. Importance of Margin of Error

Details: The margin of error is crucial in statistical inference as it provides the range for confidence intervals. A smaller margin indicates more precise estimates, while larger margins reflect greater uncertainty.

4. Using the Calculator

Tips: Enter the z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the sample proportion (between 0 and 1), and the sample size (must be ≥1).

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: What if my sample proportion is 0 or 1?
A: The formula gives error=0 in these cases, but this may underestimate true uncertainty. Consider alternative methods like Wilson score interval.

Q3: How does sample size affect the error?
A: Error decreases with the square root of sample size. Quadrupling the sample size halves the margin of error.

Q4: When is this formula appropriate?
A: When sampling with replacement, or when sample size ≤10% of population, and when np̂ and n(1-p̂) are both ≥10.

Q5: Can this be used for small samples?
A: For small samples (n < 30) or extreme p̂ values, consider exact methods like Clopper-Pearson interval.