Z-Test of a Mean

Where ${\bar {x}}$ 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:

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

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