Z-Test of a Mean

Where $\overline{x}$ is the observed mean, $e$ is the expected value, $s$ is the sample standard deviation, $n$ is the sample size, and $d_{eff}$ is Extra deff:

$z=\sqrt{n/d_{eff}}\frac{\overline{x}-e}{s}$

where $p=2(1-\mathrm{\Phi }(|z|))$ if $\overline{x}\ne e$ and NaN otherwise.