One-Sided t-Test

Test Statistic given by $T_n:=\frac{{\bar{X}}_{(n)}-{\mu }_0}{\sqrt{S_{(n)}^2/n}}$ where we estimate the Variance by the Sample Variance.

The Test Statistic has t-Distribution for $\mu ={\mu }_0$ with $n-1$ Degrees of Freedom. For $\mu \ne {\mu }_0$ we have to use the Non-Centrality Parameter $\lambda =\sqrt{n}\left(\mu -{\mu }_0\right)/\sigma .$

Confidence Interval

Confidence Interval can be calculated like this: