Complex Samples Z-Test of a Mean

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

[math]\displaystyle{ z = \frac{\bar x - e}{s_{\bar x}} }[/math]

where [math]\displaystyle{ p = 2(1-\Phi(|z|)) }[/math] if [math]\displaystyle{ \bar x \ne e }[/math] and NaN otherwise.