Work out confidence interval for mean instantly with clear inputs, formula shown and shareable results.
The confidence interval for a mean is x̄ ± t·s/√n, using the t distribution with n − 1 degrees of freedom because the population standard deviation is estimated from the sample.
Confidence interval
x̄ ± t(α/2, n−1) · s/√n
t is about 2.0452, the standard error 0.9494, so the interval is 68.4 ± 1.942, that is 66.458 to 70.342.
Estimating s from the sample adds uncertainty, so the t distribution has heavier tails; it approaches z as n grows.