Los 7.b

Question 1

What’s the central limit Theorem

Answer 1

If you take a bunch of random samples from any population (even if the population itself isn’t normally distributed), and you calculate the average (or mean) of each sample, then, as you take more and more samples, the distribution of those sample averages will look like a normal distribution (bell curve), no matter what the original population looked like.

Question 2

What are important properties of the central limit theorem?

Answer 2

If sample size n is sufficently large (greater than 30) - the sampling distribution of the sample means will be approx. normal
The mean of population and the mean of the distribution of all possible sample means are equal
The variance of the distribution of sample means is the variance / sample size

Question 3

What is the standard error of the sample mean? How is it calculated?

Answer 3

It’s the standard devation of the distribution of sample means.
Calculation: Standard devation of population / Square root of size of the sample
However, the population standard devation is rarely known, so we estimate it by: standard devation of sample /Sqauare root of size of sample