Confidence Interval Calculator

Calculate confidence intervals for population means and proportions. Understand the precision of your estimates with statistical confidence and margin of error calculations.

Quick Examples

Sample Parameters

Confidence Level

Statistical Notes

• Known σ: Uses Z-distribution
• Unknown σ: Uses t-distribution
• Proportions: Uses normal approximation
• Larger n = narrower intervals

Frequently Asked Questions

What is a confidence interval?

A confidence interval is a range of values that's likely to contain a population parameter with a certain level of confidence. It provides an estimated range of values which is likely to include the unknown population parameter.

What's the difference between 90%, 95%, and 99% confidence levels?

Higher confidence levels (99%) produce wider intervals but greater certainty that the interval contains the true parameter. Lower confidence levels (90%) produce narrower intervals but less certainty. 95% is the standard choice in most research.

When should I use t-distribution vs z-distribution?

Use z-distribution when population standard deviation is known. Use t-distribution when population standard deviation is unknown and you're using sample standard deviation instead. The t-distribution has heavier tails, accounting for additional uncertainty.

Statistical Significance

Confidence intervals provide a range of plausible values for population parameters with specified confidence levels.

Sample Precision

Larger sample sizes and lower variability lead to narrower confidence intervals and more precise estimates.

Research Applications

Essential for scientific research, market analysis, quality control, and any field requiring statistical inference.