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- Choose an interval for a mean or for a proportion.
- For a mean, enter the sample mean, standard deviation and sample size, and choose whether the SD is from the sample (t) or known for the population (z).
- For a proportion, enter the sample size and number of successes.
- Choose the confidence level.
Formel
A confidence interval is the estimate plus or minus a margin of error. When the population SD is unknown (the usual case), the critical value comes from Student's t distribution with n − 1 degrees of freedom.
Mean: x̄ ± t* × s / √n
Mean (σ known): x̄ ± z* × σ / √n
Proportion (Wilson): (p̂ + z²/2n ± z√(p̂(1−p̂)/n + z²/4n²)) / (1 + z²/n)
Example
- x̄ = 50, s = 8, n = 40, 95% confidence: t*(39) ≈ 2.0227.
- SE = 8 / √40 ≈ 1.2649; margin ≈ 2.5585.
- 95% CI ≈ 47.44 to 52.56.
Häufige Fragen
What does 95% confidence mean?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true value. It does not mean there is a 95% probability that this particular interval contains it.
When should I use t instead of z?
Use t whenever the standard deviation is estimated from your sample. For large samples (n > 100) t and z are nearly identical.
How can I make the interval narrower?
Increase the sample size (the margin shrinks with √n) or accept a lower confidence level.