Complex Samples t-Test of a Proportion

Where [math]\displaystyle{ g }[/math] is the observed proportion, [math]\displaystyle{ e }[/math] is the expected proportion, [math]\displaystyle{ s_p }[/math] is estimated Standard Error of the observed proportion and [math]\displaystyle{ n }[/math] is the sample size,

[math]\displaystyle{ n }[/math] is the sample size:

[math]\displaystyle{ t = \frac{g - e}{s_p} }[/math]

where [math]\displaystyle{ p = 2 \Pr(t_{n-1} \ge t) }[/math] if [math]\displaystyle{ g \ne e }[/math] and NaN otherwise.