Question

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 50 and σ = 18, and the mean is calculated for each sample, then the Expected Value of M is _____ and the Standard Error of M is _____?

Answer 1

Answer:

Expected Value of M is 50 and the Standard Error of M is 3

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, also called standard error $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

µ = 50 and σ = 18

For the sample

Mean 50 and standard error $s = \frac{18}{\sqrt{36}} = 3$.

The answer is:

Expected Value of M is 50 and the Standard Error of M is 3