########################################################################################
## This code is for learning concept of confidence interval
## [EMS] Chapter 6 Fig. 6.2 on page 53
## created on Nov. 2005 by Leena Choi
## modified on Jan. 13, 2007 by Leena Choi
########################################################################################

ci.95.sample <- function(n = n, n.trial=n.trial){
sam <- matrix(NA, ncol=n.trial, nrow=n)
mu <- 24.2
s <- 5
for(i in 1:n.trial){
sam[,i] <- rnorm(n, mu, s)
}
sam.mean <- apply(sam, 2, mean) 
sam.sd <- apply(sam, 2, sd)
ci.l <- sam.mean - 1.96*sam.sd/sqrt(n)
ci.u <- sam.mean + 1.96*sam.sd/sqrt(n)
sam.ci <- data.frame(mean=sam.mean, ci.l = ci.l, ci.u=ci.u)
plot(1:n.trial, sam.mean, xlab="Identification number of trial", ylab="Sample mean and 95% CI", xlim=c(1, n.trial+1.6), ylim=c(21, 27), pch=19)
abline(h=mean(sam.mean), lty=2, col=3)
text((n.trial+1.1), 24.4, labels = paste("\m","=",mu), vfont=c("serif symbol", "plain"), cex=1.2, col=3)
for(i in 1:n.trial){
segments(i, ci.l[i], i, ci.u[i])
}
}

## change the sample size n
n.trial <- 20
n <- 100
set.seed(16)
ci.95.sample(n = n, n.trial=n.trial)
text(7, 26.4, "*", col=2, cex=2)