#Coverage of Confidence Intervals, Normal Population, Known Population SD, sigma=1.
#Sample size n
#Population Mean mu=0
#Generate 100 samples, Plot CI. A CI that covers mu is black. A CI that does not cover mu is blue.
#
par(mfrow=c(2,1))
n=25
NumFailures=0
plot(1:100,type="n",ylim=c(-1,1),xlab="",ylab="")
abline(h=0)
seed=trunc(100000*runif(1))
#print(seed)
set.seed(seed)
for(iter in 1:100)
  {xbar=mean(rnorm(n))
   Lower=xbar-1.96*1/sqrt(n)
   Upper=xbar+1.96*1/sqrt(n)
   if((Upper<0)||(Lower>0))
   {NumFailures=NumFailures+1;segments(iter,Lower,iter,Upper,col="red")}
   else segments(iter,Lower,iter,Upper)}
#
title(main=paste("95% CIs for the mean, Normal Population, n=",n,", sigma=1
True Mean is Zero. Failed Intervals in Red. Failure Rate =",NumFailures/100))
#
set.seed(seed)
NumFailures=0
plot(1:100,type="n",ylim=c(-1,1),xlab="",ylab="")
abline(h=0)
for(iter in 1:100)
  {xbar=mean(rnorm(n))
   Lower=xbar-2.576*1/sqrt(n)
   Upper=xbar+2.576*1/sqrt(n)
   if((Upper<0)||(Lower>0))
   {NumFailures=NumFailures+1;segments(iter,Lower,iter,Upper,col="red")}
   else segments(iter,Lower,iter,Upper)}
#
title(main=paste("99% CIs for the mean, Normal Population, n=",n,", sigma=1
True Mean is Zero. Failed Intervals in Red. Failure Rate =",NumFailures/100))
#
#print(seed)
#