One-Sided t-Test

Test Statistic given by

Tn:=Xˉ(n)−μ0S(n)2/nT_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 μ=μ0\mu=\mu_0 with n−1n-1 Degrees of Freedom.
For μ≠μ0\mu\neq\mu_0 we have to use the Non-Centrality Parameter

λ=n(μ−μ0)/σ.\lambda=\sqrt{n}\left(\mu-\mu_0\right) / \sigma.

Confidence Interval

Confidence Interval can be calculated like this:

Bildschirm­foto 2023-02-10 um 10.55.34.png