set.seed(123)

CIlower<-numeric(10000)
CIupper<-numeric(10000)
pvalue1<-numeric(10000)
pvalue2<-numeric(10000)

for(j in 1:10000) {
  (sample<-rnorm(100,10,2))
  (s2<-var(sample))
  (chi<-(99*s2)/4)
  (pvalue1[j]<-pchisq(chi, 0.975, df=99, lower.tail=F))
  (pvalue2[j]<-pchisq(chi, 0.025, df=99, lower.tail=T))
  (chi_u<-qchisq(0.975, df=99))
  (chi_l<-qchisq(0.025, df=99))
  (CIlower[j]<-(99*s2)/chi_u)
  (CIupper[j]<-(99*s2)/chi_l)
}

#CIlower
#CIupper
#pvalue1
#pvalue2

reject1<-pvalue1 <= 0.025 | pvalue2 <= 0.025
table(reject1)

color<-rep(gray(.7),100)
color[reject1[1:100]]<-"black"

plot(0, xlim=c(1,7), ylim=c(1,100), ylab="Sample No.", xlab="", main="95% Confidence Interval for sigma-square")
abline(v=4, lty=2)
for(j in 1:10000) {
  lines(c(CIlower[j], CIupper[j]), c(j,j), col=color[j], lwd=1)
}