Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 3 / 18H / a / Solution

For $\overline X\sim N(\mu,1/n)$ under $H_0:\mu=0$, the two-sided level-$\alpha$ test rejects when $|\sqrt n\,\overline X|>\Phi^{-1}(1-\alpha/2)$, and the observed p-value is
$$
p(\overline x)=2[1-\Phi(\sqrt n|\overline x|)].
$$


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 Incoming links: Two-sided Gaussian p-value