T-Test of a Probability %

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Where [math]\displaystyle{ \hat{a} }[/math] is a probability % from a ranking question, [math]\displaystyle{ \mu }[/math] is the mean probability %, [math]\displaystyle{ n }[/math] is the effective number of observations (note that this is different to the effective sample size where repeated observations exist for each respondent) and [math]\displaystyle{ se_{a} }[/math] is the standard error of [math]\displaystyle{ \hat{a} }[/math], the test statistic is:

[math]\displaystyle{ t=\frac{\hat{a}-\mu}{se_{a}} }[/math],


[math]\displaystyle{ p = 2\Pr(t_{n-k+1} \ge |t|) }[/math],
[math]\displaystyle{ k }[/math] is the number of alternatives.