For a <critical region> $C$, the <size of a statistical test> of the simple <null hypothesis> $P_0$ is $\alpha=P_0(\boldsymbol X\in C)$, the <Type I error> probability. Its <statistical power> against the simple <alternative hypothesis> $P_1$ is $P_1(\boldsymbol X\in C)$, the probability of correctly rejecting that null. For a randomized test function $\varphi(\boldsymbol x)\in[0,1]$, replace these by $\mathbb E_0\varphi$ and $\mathbb E_1\varphi$.

Solution

Past exam of the statistics course of the University of Oxford / 2023 / 2 / a / i / Solution

 Solution (source code)