## simulate a bunch of confidence intervals to illustrate coverage
## ADM 10/7/2007
set.seed(1234)

## toss N coins and count the number of heads
N <- 50

## repeat simulation G times
G <- 100

## vector of draws
draws <- rbinom(G,N,0.5)/N

## look at the draws
hist(draws, freq=FALSE)

## compute 95% confidence intervals
SE <- sqrt(draws * (1-draws)/N)

## plot the correct 95% confidence intervals
matplot(rbind(draws - 1.96 * SE, draws+1.96*SE), rbind(1:G, 1:G),
   type="l", lty=1, xlab="Proportion", ylab="Draw")
abline(v=.5)

## plot incorrect 95% confidence intervals (just one SE)
matplot(rbind(draws - 1 * SE, draws+1*SE), rbind(1:G, 1:G),
   type="l", lty=1, xlab="Proportion", ylab="Draw")
abline(v=.5)