T-Test of a Probability %

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

$t=\frac{\hat{a}-\mu }{s{e}_a}$,

where:

$p=2\mathrm{Pr}(t_{n-k+1}\ge |t|)$,

$k$ is the number of alternatives.