conf_int_validity.R

library(ggplot2)

observations <- 5
mu = 10
trials <- 100

confidence.interval <- function(threshold = .975, variance = 4) {
  x <- rnorm(observations, mean = mu, sd = sqrt(variance))
  df <- length(x) - 1
  SE <- sd(x) / sqrt(length(x))
  c(mean(x) - qt(threshold, df) * SE,
    mean(x) + qt(threshold, df) * SE)
}


p <- ggplot()
for (i in seq(trials)) {
  ci <- confidence.interval()
  if (ci[1] > mu | ci[2] < mu)
    col <- 'red'
  else
    col <- 'green'
  p <- p + geom_line(aes_string(c(i, i), ci), colour=col)
}
p + xlab('x') + ylab('interval')