Also see <http://stat.ethz.ch/R-manual/R-devel/library/stats/html/prop.test.html>
Nice math introhttps://onlinecourses.science.psu.edu/statprogram/node/164 with t-statistc
Confidence around proportions
-----------------------------
Formula:
> If the samples size n and population proportion p satisfy the condition that np ≥ 5 and n(1 − p) ≥ 5, than the end points of the interval estimate at (1 − α) confidence level is defined in terms of the sample proportion as follows.

CI math is detailed out under http://www.statisticslectures.com/topics/ciproportions/
Also see <http://stat.ethz.ch/R-manual/R-devel/library/stats/html/prop.test.html>
Nice math introhttps://onlinecourses.science.psu.edu/statprogram/node/164 with t-statistc
Confidence around proportions
-----------------------------
Formula:
> If the samples size n and population proportion p satisfy the condition that np ≥ 5 and n(1 − p) ≥ 5, than the end points of the interval estimate at (1 − α) confidence level is defined in terms of the sample proportion as follows.
CI math is detailed out under http://www.statisticslectures.com/topics/ciproportions/