3. The file "Sampling Distribution.xlsx" is a guided exercise on how to simulate the distribution of the sample mean. Before starting the exercise, we encourage you to play with this pre-programmed simulation as it will give you a sense of what you are aiming for. The "Steps" sheet contains the instruction to perform the simulation. The "Population" sheet has the universe of observations 500 observations denoted with the variable name X. The "Sample" sheet in where you are supposed to perform the simulation. The idea is to draw 30 random samples of the population, each sample with 19 observations. You will compute the mean for each random sample, i.e., the sample mean. a) What is the population mean of X? b) What is the population variance of X? c) Draw a histogram of X for the entire population. d) What is the average of the 30 sample means you simulated? e) What is the variance of the 30 sample means you simulated? f) Draw a histogram of the 30 sample means you simulated. g) Compare the population mean E(X) with the mean of the sample mean E(X). h) Compare the population variance Var(X) with the variance of the sample mean Var(X). i) What would happen if you increased the number of random samples from 30 to 40? To 50? To 100? j) What would happen if you increased the sample size from 19 to 30, 50, 100?