p-Value

Acceptance Domain $A_{\alpha }$ $p(t)=\inf \left\{\alpha \in (0,1):t\notin A_{\alpha }\right\}$

Interpretation

• Smallest level $\alpha$ which leads to rejecting the Null Hypothesis.
• <

High p-Value of $y$ means that $y$ is typical of random variable $Y$.

For example for an Exponential Distribution small $y$ are more typical. We thus define the p-Value as $p(y)=P(Y\ge y)$ which is small question.

todo Second example with Normal Distribution

For Gauß Test:

• at $\mu ={\mu }_0$ we have Uniform Distribution on $(0,1)$ for the p-Value

Left-sided

Right-sided Two-sided