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

5

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 = (\sigma)/(√(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 = (\sigma)/(√(n)) = (20)/(√(16)) = 5`

The answer is 5.