Question

i.Bias of Sample Mean Draw 20 samples from the normal distribution N(5, 4). Compute the mean of your 20 samples. Report the bias of the sample mean

ii. Variance of Sample Mean (Continue of problem i) To estimate the variance of the sample mean, we need to draw many different samples of size 20. Now, we draw 1000 times a sample of size 20. Store all the 1000 sample means. Report the variance of the estimated sample mean. Hint: To draw the samples 1000 times, we need to use ”for loop” in R. Firstly we create a vector of length 1000. Then we store each sample mean into the vector. Then you can estimate the variance of the sample mean with the variance function in R. sample.mean = rep(0, 1000) for(i in 1:1000) { s1 = rnorm(20, mean, sd) sample.mean[i] = mean(s1)

iii.

Answer 1