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 $se_{a}$ is the standard error of $\hat{a}$, the test statistic is:

$t=\frac{\hat{a}-\mu}{se_{a}}$,

where:

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

$k$ is the number of alternatives.