Confidence Interval

Confidence interval for a mean or proportion

95% CI for μ: x̄ ± t* · s/√n = 50 ± t* · 10/√30
Confidence interval
[46.2659, 53.7341]
Sample mean (x̄)
50
Margin of error
± 3.7341
Standard error
1.825742
t* (df 29)
2.0452
Lower limit
46.2659
Upper limit
53.7341
Method
Student-t interval (σ unknown)
Confidence intervalNumber line showing the 95% confidence interval from 46.2659 to 53.7341, centered on the point estimate 50.95%5046.265953.7341± 3.7341

この計算機について

The Confidence Interval Calculator builds a two-sided confidence interval for a population mean or a population proportion. For a mean it uses the Student-t interval x̄ ± t* · s/√n with df = n − 1; for a proportion it uses the normal (Wald) interval p̂ ± z* · √(p̂(1−p̂)/n). Enter your sample statistics and confidence level to get the margin of error, the lower and upper limits, the critical value, and the standard error, with a number-line diagram of the interval. Useful for statistics, polling, A/B testing, and lab measurements.

一般的な例

  • Mean: x̄ = 50, s = 10, n = 30, 95% → 50 ± 3.73 = [46.27, 53.73]
  • Proportion: 45 of 100, 95% → 0.45 ± 0.098 = [0.352, 0.548]
  • A higher confidence level (99%) widens the interval; a larger sample (n) narrows it
  • Poll of 60%, n = 1000, 95% → 0.60 ± 0.030 = [0.570, 0.630]
  • Small sample n = 5 uses a wider t* than the normal z* for the same confidence