set.seed(1)

N<-100000
height.male<-rnorm(N,69.5,2.75)  # 5 foot, 9.5 inches
height.female<-rnorm(N, 64.5, 2.75)  # 5 foot, 4.5 inches

par(mfrow=c(2,1))
hist(height.male, freq=FALSE, xlim=c(55,80))
hist(height.female, freq=FALSE, xlim=c(55,80))


n<-5

height.male.sample<-rnorm(n,69.5,2.75)
height.female.sample<-rnorm(n,64.5,2.75)

t.test(height.male.sample,height.female.sample)

pval<-NULL
for (i in 1:1000) {
  height.male.sample<-rnorm(n,69.5,2.75)
  height.female.sample<-rnorm(n,64.5,2.75)
  pval[i]<-t.test(height.male.sample,height.female.sample)$p.value
}


sum(pval<.05)/1000




N<-100000
height.male.white<-rnorm(N,70.5,2.75)  # 5 foot, 10.5 inches
height.male.latino<-rnorm(N, 67, 2.75)  # 5 foot, 7 inches

par(mfrow=c(2,1))
hist(height.male.white, freq=FALSE, xlim=c(55,80))
hist(height.male.latino, freq=FALSE, xlim=c(55,80))


n<-20

height.male.white.sample<-rnorm(n,70.5,2.75)
height.male.latino.sample<-rnorm(n,67,2.75)

t.test(height.male.white.sample,height.male.latino.sample)

pval<-NULL
for (i in 1:1000) {
  height.male.white.sample<-rnorm(n,70.5,2.75)
  height.male.latino.sample<-rnorm(n,67.5,2.75)
  pval[i]<-t.test(height.male.white.sample,height.male.latino.sample)$p.value
}


sum(pval<.05)/1000





prob.dis.treat<- 0.2
prob.dis.control<-0.3

n<-20
pval<-NULL
for (i in 1:1000) {
  dis.treat<-rbinom(1,n,prob.dis.treat)
  dis.control<-rbinom(1,n,prob.dis.control)
  pval[i]<-chisq.test(matrix(c(dis.treat,n-dis.treat,dis.control,n-dis.control),nrow=2))$p.value
}

sum(pval<.05)/1000