#Initialize vectors p1hat and p2hat:
p1hat <- rep(0,1000)
p2hat <- rep(0,1000)

#Data from sample 1:
x1 <- c("yes", "yes", "yes", "yes","yes", "no", "no", "no", "yes","no")

#Data from sample 2:
x2 <- c("yes", "yes", "no", "no","no", "no", "no", "no", "no","no")

#We want to test H0: p1-p2=0 Vs. Ha: p1-p2 != 0.
#Under H0 we treat the data as one sample:

x3 <- c(x1,x2)

#We will shuffle the data in x3 and randomly select n1=10 each time to compute the simulated p1_hat.  Similarly we compute p2_hat:
 
#A for loop that will split the data into two parts:
for(i in 1:1000){
	y1 <- sample(x3, 10)
    p1hat[i] <- sum(y1=="yes")/10
    p2hat[i] <- (sum(x3=="yes")-sum(y1=="yes"))/10
}

#Construct a histogram using the 1000 simulated p1_hat-p2_hat:

pdiff_hat <- p1hat - p2hat

hist(pdiff_hat, breaks=seq(-1, 1,.20))

#Find p1_hat-p2_hat from the original data:
pdiff_hat_orig <- sum(x1=="yes")/10 - sum(x2=="yes")/10

#Place it on the histogram:
segments(pdiff_hat_orig ,0,pdiff_hat_orig ,300, col="green")

#Compute p-value:
2*sum(pdiff_hat > pdiff_hat_orig)/1000