Question

(Q5.1) Consider the samples {1, 2, 3, 4, 5, 6}. Using a random number generator, obtain three different bootstrap samples and their respective means. What is the bootstrap estimate of the standard error of the sample mean using these three replicates?

Answer 1

IN R

Firstly let us feed in the data:

dat <- c{1,2,3,4,5,6}

Generate 3 bootstrap replications and their respective means:

n <- length(dat) #n=6

B <- 3

boot <- numeric(B)

for (i in 1:B) { idx <- sample(1:n, size = n, replace = TRUE) #choose 8 indices with replacement

boot[i] <- mean(sort(dat[idx])[3:6])​​​​​​​ #draw sample, compute & store trimmed mean

}

Compute bootstrap estimate of standard error:

se <- sd(boot)

cat("Bootstrap estimate of standard error is", se)