1. What is Sample Error?

Sample error (margin of error) represents the range within which the true population parameter is expected to fall. It quantifies the uncertainty in sample estimates when making inferences about a population.

2. How Does the Calculator Work?

The calculator uses the sample error equation:

Where:

• \( z \) — Z-score corresponding to the desired confidence level
• \( \sigma \) — Population standard deviation
• \( n \) — Sample size

Explanation: The equation shows that error decreases as sample size increases, and increases with greater variability in the population.

3. Importance of Sample Error Calculation

Details: Calculating sample error is essential for determining the reliability of statistical estimates, designing studies with appropriate sample sizes, and interpreting confidence intervals correctly.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: What if I don't know the population standard deviation?
A: For large samples (n > 30), you can use the sample standard deviation as an estimate.

Q3: How does sample size affect the error?
A: Error is inversely proportional to the square root of sample size - quadrupling the sample size halves the error.

Q4: What's the difference between standard error and margin of error?
A: Standard error is σ/√n, while margin of error multiplies this by the Z-score to create a confidence interval.

Q5: When is this formula not appropriate?
A: For small samples (n < 30) from non-normal distributions, consider using t-scores instead of Z-scores.