A random sample of n = 4 scores is selected from a population with ƒÝ = 80 and ƒã = 20. On average, how much difference would you expect between the sample mean and the population mean?

a. 0 points (the sample mean should be the same as the population mean)
b. 5 points
c. 10 points
d. 80 points

Plus or minus a standard error of the mean (SEm) encompasses approximately 68% of the probable scores.

SEm = SD/√n

To determine how much of a difference between the sample mean and population mean is expected, we need to use the standard error of the mean. The standard error of the mean measures the variability or dispersion of sample means around the population mean.

The formula for the standard error of the mean is:

Standard Error of the Mean (SE) = σ / √n

Where:
- σ (sigma) is the standard deviation of the population.
- n is the sample size.

In this case, we are given that the population standard deviation (σ) is 20 and the sample size (n) is 4.

Using the formula, we can calculate the standard error of the mean:

SE = 20 / √4 = 20 / 2 = 10

So, the standard error of the mean is 10. This means that on average, we would expect the sample mean to differ from the population mean by approximately 10 points.

Therefore, the answer is c. 10 points.