I am wondering what approaches are used in R to find the confidence interval for proportion? For example, in prop.test, it provides a confidence interval which is different from $\bar{p}-+z_{\alpha/2} \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$.
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binom.test()in thestatspackage, which - in contrast to the approaches mentioned there - belongs to the standard installation of R. – Michael M Feb 15 '22 at 18:17