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?

5

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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:

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 . So

The answer is 5.

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