# T-Test of a Probability %

Where ${\displaystyle {\hat {a}}}$ is a probability % from a ranking question, ${\displaystyle \mu }$ is the mean probability %, ${\displaystyle n}$ is the effective number of observations (note that this is different to the effective sample size where repeated observations exist for each respondent) and ${\displaystyle se_{a}}$ is the standard error of ${\displaystyle {\hat {a}}}$, the test statistic is:
${\displaystyle t={\frac {{\hat {a}}-\mu }{se_{a}}}}$,
${\displaystyle p=2\Pr(t_{n-k+1}\geq |t|)}$,
${\displaystyle k}$ is the number of alternatives.