CLT Practice

Practice Problems

Instructions

Answer the following questions, render the document and submit the .html report.

Questions

Suppose you take a sample of size \(n=5\) from a right skewed distribution with a population mean, \(\mu=125\) and a standard deviation, \(\sigma=12\)

Question: What is the mean of the distribution of sample means (\(\mu_{\bar{x}}\))?
Answer:

Question: What is the standard deviation of sample means (\(\sigma_{\bar{x}}\))?
Answer:

Question: What is the shape of the distribution of sample means and why?
Answer:

Now suppose you increase the sample size to \(n=100\). What is:

Mean of sample means:
Standard deviation of sample means:
Shape of the distribution of sample means:

Describe the difference between the Law of Large Numbers and the Central Limit Theorem.
Answer: