Question

For a population, a sample of n = 36 scores has a standard error (σM) of 3. For the same population, a sample of n = 81 would have a standard error of what?

A) 1.5
B) 3
C) 1
D) 2

Answer 1

For the same population where a sample of n = 36 has a standard error of 3, the standard error for a sample of n = 81 would be 2, which is option D.

Step-by-step explanation:

The student asks for the standard error of the mean for a different sample size using the same population. With an initial sample (n = 36) having a standard error (σM) of 3, to find the standard error for a larger sample (n = 81), we use the formula for standard error of the mean, which is σM = σ / √n, where σ is the population standard deviation and n is the sample size. Considering that for n = 36, σM is 3, we can infer that the population standard deviation (σ) is σM * √n = 3 * √36 = 3 * 6 = 18. We can now calculate the standard error for n = 81 using the found population standard deviation:

• σM = σ / √n = 18 / √81 = 18 / 9 = 2

Thus, the standard error for a sample size of n = 81 would be 2, which corresponds to option D.