Question

Given the population 5, 10, 15, 20, 25

a) How many samples of size 3, can be drown with replacement from this population

b) Compute and tabulate the sampling distribution of the mean from samples of size 3.

c) Verify the results of mean and variance of sampling distribution of mean.​

Answer 1

Explanation:

a) List all possible samples of size n = 3, with replacement, from the population {1,3,5}. 2 = 8/3, and standard deviation σ = √8/3≈1.633 of the population.

b)For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n, where n is the sample size.

c) The mean and variance of the sampling distribution of the mean for a Gaussian distribution are mu and sigma/sqrt(n) (i.e., Standard Error), but I have been trying to find out how to derive the mean and variance of the sampling distribution of the standard deviation. I have been directed towards using the Central Limit Theorem (CLT), but I have not had much success so far.