CS1B 201909 1iv)

[singingmyblues]

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)

 

[singingmyblues]

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)))