Two-sided Gaussian p-value
= Two-sided Gaussian p-value
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
$$
p(\overline x)=2[1-\Phi(\sqrt n|\overline x|)].
$$