Question

For a population, a sample of n = 25 scores has a standard error (σM) of 4. For the same population, a sample of n = 16 would have a standard error of what?

a. 2.67
b. 3
c. 3.5
d. 4.5

Answer 1

The standard error for a sample of size n = 16 is 5.

Step-by-step explanation:

To find the standard error for a sample of size n = 16, we can use the formula:

Standard Error (σM) = Standard Deviation (σ) / √Sample Size (n)

Given that the standard error (σM) for a sample of size n = 25 is 4, we can plug in these values:

4 = σ / √25

Now solving for σ, we get:

σ = 4 × √25 = 4 × 5 = 20

Substituting this value into the formula for a sample of size n = 16:

Standard Error (σM) = 20 / √16

Calculating this, we get:

Standard Error (σM) = 20 / 4 = 5

Therefore, the standard error for a sample of size n = 16 would be 5.