Math 239 Problem Set #2

Question 5e

x1<-69
n1<-100
x2<-17
n2<-30

p_hat1<-x1/n1
p_hat2<-x2/n2

pooled<-(x1+x2)/(n1+n2)

#sample z-test for prop (see setup for this above)
test_stat<-(p_hat1-p_hat2)/sqrt(pooled*(1-pooled)*(1/n1+1/n2)) #p-value

#two-tailed
pnorm(test_stat, lower.tail=FALSE)*2 #false shades upper tail

## [1] 0.2105353

#CONFIDENCE INTERVAL
critVal<-qnorm(0.975)
SE<-sqrt(p_hat1*(1-p_hat1)/n1+p_hat2*(1-p_hat2)/n2)

(p_hat1-p_hat2)+c(-1,1)*critVal*SE

## [1] -0.07581468  0.32248135

#RANDOMIZATION / PERMUTATION
nsim=1000
Populations<-c(rep("A",100), rep("T",30))
Follow<-c(rep("Yes",86), rep("No",44))
Popdif<-rep(NA, nsim)

for(i in 1:nsim){
  permuteGen<-sample(Populations) #putting everyting in a bin
  tab<-table(permuteGen, Follow) #creates table
  Popdif[i]<-diff(tab[,2]/130)
}

hist(Popdif)