#Parameters to simulate sample 1 from a normal population
n1 _ 30
mu1 _ 100
sigma1 _ 10

#Parametets to simulate sample 2 from a normal population
n2 _ 30
mu2 _ 100
sigma2 _ 15

#m denotes the number of simulated F-tests
m _ 10

alpha _ .05
Fvector _ c()
pvector _ c()

for(i in 1:m) {
	x _ rnorm(n1,mu1,sigma1)
	y _ rnorm(n2,mu2,sigma2)
	F.output _ var.test(x, y, alternative = "two.sided", conf.level=.95)
	Fstat _ F.output$statistic
	pvalue _ F.output$p.value
	Fvector _ c(Fvector,Fstat)
	pvector _ c(pvector, pvalue)
}

sig.level _ length(pvector [pvector < .05])/m
print(sig.level)
hist(Fvector,nclass=20,probability=T)
hist(pvector, nclass=20, breaks = seq(0,1,.05))
summary(pvector)
print(sqrt(var(pvector)))

bounds.f_qf(.999,29,29)
points.x_seq(0,bounds.f,length=1000)
points.y_df(points.x,29,29)
plot(points.x,points.y,type="l",xlim=range(c(points.x)),ylim=range(c(points.y)),
		xlab="F-distribution",ylab="")