Question

A sample of n = 16 scores is selected from a population with LaTeX: \muμ = 80 with LaTeX: \sigmaσ = 20. On average, how much error would be expected between the sample mean and the population mean?

Answer 1

Answer:

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:

$\mu = 80, \sigma = 20$

On average, how much error would be expected between the sample mean and the population mean?

This is the standard deviation of the sample. We have that $n = 16$. So

$s = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{16}} = 5$

The answer is 5.