Confidence Interval Calculator Information
What is a Confidence Interval?
A confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter (mean or proportion) with a specified probability (confidence level).
- CI = Confidence interval
- x̄ = Sample mean
- z = Z-score for confidence level
- σ = Population standard deviation
- n = Sample size
Example: x̄ = 50, σ = 10, n = 25, 95% confidence (z = 1.96)
CI = [46.08, 53.92]
Why Use Confidence Intervals?
- Statistics: Estimate population parameters from samples
- Research: Report uncertainty in survey or experiment results
- Business: Make data-driven decisions with known margins of error
- Science: Communicate reliability of findings
Tips for Calculating Confidence Intervals
- Choose the Right Formula: Use z for large samples, t for small samples or unknown σ
- Check Assumptions: Data should be random and (for means) approximately normal
- Interpret Correctly: A 95% CI means 95% of such intervals will contain the true value
- Report Both Bounds: Always give the full interval, not just the margin
Frequently Asked Questions (FAQ)
A: It means that 95% of intervals calculated from repeated samples will contain the true parameter.
A: Use t for small samples (n < 30) or unknown σ; use z for large samples with known σ.
A: Yes, use the formula for proportions: CI = p̂ ± z × √[p̂(1-p̂)/n]
A: For non-normal data, use bootstrapping or nonparametric methods.
A: The margin added/subtracted from the estimate to create the interval.
Important Disclaimers
Disclaimer: This calculator provides estimates for educational purposes only. Confidence intervals are based on statistical assumptions that may not hold for all datasets.
Always verify that your data meets the assumptions for the chosen confidence interval method. For critical applications, consult with a qualified statistician or use professional statistical software.
This calculator is not a substitute for professional statistical analysis. Results should be interpreted in the context of your specific research question and methodology.