Confidence Interval Calculator

What a 95% confidence interval means

It does not mean there is a 95% chance the true value is in this particular range. It means the method produces an interval that captures the true value 95% of the time across repeated samples. In practice: report the interval, not just the point estimate — “12% ± 3” is honest, “12%” alone pretends to a precision you don't have.

Why the mean uses t, not z

When you estimate the standard deviation from the sample (you almost always do), the t-distribution accounts for that extra uncertainty — its intervals are slightly wider for small samples and converge to the normal (z) result as n grows. Using z on a small sample understates the interval, which is the common mistake this avoids.