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:

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

$k$ is the number of alternatives.