Question

For a population with µ = 80 and σ = 20, the Sampling distribution of the Mean, based on n = 16 will have an expected value of the mean = ____ and a standard error of the mean = ____

Answer 1

Answer:

Will have an expected value of the mean = 80 and a standard error of the mean = 5

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 $s = \frac{\sigma}{\sqrt{n}}$.

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:

$\mu = 80, \sigma = 20$

n = 16

So the mean is 80 and the standard deviation is $s = \frac{20}{\sqrt{16}} = 5$

Will have an expected value of the mean = 80 and a standard error of the mean = 5