  We study the following fundamental hypothesis testing problem, which we term
Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on
$\mathbb{R}^d$, the task is to distinguish, with high probability, between the
following cases: (i) $p$ is the standard Gaussian distribution,
$\mathcal{N}(0,I_d)$, and (ii) $p$ is a Gaussian $\mathcal{N}(\mu,\Sigma)$ for
some unknown covariance $\Sigma$ and mean $\mu \in \mathbb{R}^d$ satisfying
$\|\mu\|_2 \geq \epsilon$. Recent work gave an algorithm for this testing
problem with the optimal sample complexity of $\Theta(\sqrt{d}/\epsilon^2)$.
Both the previous algorithm and its analysis are quite complicated. Here we
give an extremely simple algorithm for Gaussian mean testing with a one-page
analysis. Our algorithm is sample optimal and runs in sample linear time.
