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# Hypothesis Testing: significance level (alpha), Type One Error

mu <- 0		# population mean, mu, for the "unknown" population
sigma <- 2		# population standard deviation, sigma, for the "unkown" population

n <- 30		# sample size
k <- 1000		# number of samples 

x <- matrix(rnorm(n*k,mu,sigma),n,k)		# This gives a matrix with k = 1000 samples down the columns.

alpha <- 0.05		# significance level

Count <- 0 		# count the number of times reject the null hypothesis

# next is a loop that computes the one sample t test for each of the k random samples
# and it computes the number of times the null hypothesis is rejected.

for(j in 1:k){	
	x.test <- t.test(x[,j]) 
	if(x.test$p.value < alpha) Count <- Count + 1
}

alpha.est <- Count/k		# estimated the significance level
alpha.est		# alpha.est should be approximately equal to alpha