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

#A total of 2230 boys and 1937 girls born:
nboys <- 2230 
ngirls <- 1937

#Create a vector of 2230 boys:
x1 <- rep("boy", nboys)

#Create a vector of 1937 girls:
x2 <- rep("girl", ngirls)

#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=3602 and n2=565 each time to compute the simulated p1hat and p2hat.

#Shuffle the x3 vector:
x33 <- sample(x3)

n1<- 3602
n2 <- 565 
n <- n1+n2



















#A for loop that will split the data into two parts:
for(i in 1:1000){
        choose_n1 <- sample(1:n, n1)
	y1 <- x33[choose_n1]
        y2 <- x33[-choose_n1]
    p1hat[i] <- sum(y1=="boy")/n1
    p2hat[i] <- sum(y2=="boy")/n2
}

#Construct a histogram using the 1000 simulated differences p1hat-p2hat:
pdiff_hat <- p1hat - p2hat

hist(pdiff_hat, xlim=c(-0.1, 0.1), main="Histogram of 1000 simulated p1hat-p2hat values", xlab="pdiff_hat = p1hat-p2hat")

#Find p1_hat-p2_hat from the original data:
pdiff_hat_orig <- 1975/3602 - 255/565

#Place it on the histogram:
points(pdiff_hat_orig , 0, pch=19, col="green")

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