wald = function (x,n,alpha) {
 z=-qnorm(alpha/2) ; phat = x/n ; se=sqrt(phat*(1-phat)/n);
 c(phat-z*se,phat+z*se) }
wald(x=23,n=89,alpha=.05)            # Wald Interval
prop.test(x=23,n=89,correct=F)       # Wilson Interval
agresti.coull = function (x,n,alpha) {
 z=-qnorm(alpha/2); ntilde = n+z^2 ; ptilde = (x+z^2/2)/ntilde ;
 se=sqrt(ptilde*(1-ptilde)/ntilde);
 c(ptilde-z*se,ptilde+z*se)}
agresti.coull(x=23,n=89,alpha=.05)   # Agresti-Coull Interval