Confidence Interval Calculator

It means that 95% of all confidence intervals constructed from repeated samples of the same size would contain the true population parameter. It does not mean there is a 95% probability that the true mean falls within this specific interval — once calculated, it either does or does not.

Larger samples produce narrower confidence intervals because the standard error (σ/√n) decreases as n increases. Doubling the sample size reduces the margin of error by a factor of √2 ≈ 1.41. This is why large surveys provide more precise estimates than small ones.

Use 99% confidence intervals when the cost of being wrong is very high — medical studies, structural engineering, legal evidence. Use 95% for most research. The trade-off is that higher confidence requires a wider interval, which is less precise and sometimes less useful for decision-making.