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 $\mu\neq\mu_0$ 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:

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