Complex Samples Z-Test of a Mean

Where ${\bar {x}}$ is the observed mean, $e$ is the expected value, $s_{\bar {x}}$ is the estimated Standard Error of the observed mean and $n$ is the sample size:

$z={\frac {{\bar {x}}-e}{s_{\bar {x}}}}$

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