Checking prop.test (confidence interval of the proportion)

check_prop.R

set.seed(1234)
n <- 12
x <- rbinom(1,n,0.5)
res_p <- prop.test(x, n, p = 0.5, correct = FALSE)

CI_score <- function(x, n, level){
  z <- qnorm(0.5*(1-level), lower.tail = FALSE)
  phat <- x/n
  t_1 <- phat+(z^2)/(2*n)
  t_2 <- sqrt(z^2+4*n*phat*(1-phat))*(z/(2*n))
  c((t_1 - t_2)/(1+(z^2)/n),
    (t_1 + t_2)/(1+(z^2)/n))  
}


print(CI_score(x,n,0.95))
print(res_p$conf.int)

#cf.
res_b <- binom.test(x, n, p = 0.5)
print(res_b$conf.int)