The question asks us to comment on the difference between confidence intervals, created in a bootstrap vs parametric way. Why would you say the bootstrap CI is smaller is because the distribution of X is not normal (the examiner report says this)? I think it can be because the bootstrap is using a bigger sample of 10000 (the bootstrapped sample created using replicate) whereas the t.test sample is just length(x)
another question in 201909 3iv) I seem to get different results running set.seed(2019) y = 0*(1:1000) # generate a vector of size 1000 for (i in 1:1000){ y = sum(rexp(15, 2)) } and set.seed(2019) # Parameters n <- 15 lambda <- 2 B <- 1000 # Generate Bootstrap samples bootstrap_samples_Y <- replicate(B, sum(sample(rexp(n, lambda), replace = TRUE)))
