For a population with a mean of μ � 70 and a standard

deviation of � � 20, how much error, on average,
would you expect between the sample mean (M) and
the population mean for each of the following sample
sizes?
a. n � 4 scores
b. n � 16 scores
c. n � 25 scores

Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.

To determine how much error, on average, we would expect between the sample mean (M) and the population mean, we can use the standard error of the mean formula.

The standard error of the mean (SE) is calculated by dividing the standard deviation (σ) by the square root of the sample size (n).

SE = σ / √n

Let's calculate the standard error for each of the given sample sizes:

a. For a sample size of n = 4 scores:
SE = 20 / √4 = 20 / 2 = 10

Therefore, for a sample size of 4 scores, we would expect an average error of 10 between the sample mean and the population mean.

b. For a sample size of n = 16 scores:
SE = 20 / √16 = 20 / 4 = 5

Therefore, for a sample size of 16 scores, we would expect an average error of 5 between the sample mean and the population mean.

c. For a sample size of n = 25 scores:
SE = 20 / √25 = 20 / 5 = 4

Therefore, for a sample size of 25 scores, we would expect an average error of 4 between the sample mean and the population mean.