After years of "abstinence" I dabble back into statistics of population proportions and have some trouble making sense of critical values $z^\star$ for high confidence levels:
The critical value $z^\star$ is needed for the calculation of confidence intervals. I compute $z^\star$ from the confidence level cl with the Python module
cdf = 0.5+cl/2 z_star = scipy.stats.norm.ppf(cdf)
z_star (i.e. $z^\star$) can grow to infinity, because
On the other hand, I'd say the confidence interval
$CI= \hat p \pm z^\star se(\hat p)$
can reasonably not exceed $[0\%,100\%]$.
How do these things fit together?
- Is the
scipycalculation an approximation with goes astray for confidence levels close to $100\%$?
- Or is my idea that confidence intervals not exceed $[0\%,100\%]$ not general enough?
- Or is something with my
I would love some pointers here!