Question

Which of the following would produce a standard error of 2 points? n = 5 scores from a population with σ = 20 n = 5 scores from a population with σ = 80 n = 100 scores from a population with σ = 20 n = 100 scores from a population with σ = 40

Answer 1

Answer:

n = 100 scores from a population with σ = 20

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error, of $s = \frac{\sigma}{\sqrt{n}}$

n = 5 scores from a population with σ = 20

$s = \frac{20}{\sqrt{5}} = 8.94$

n = 5 scores from a population with σ = 80

$s = \frac{80}{\sqrt{5}} = 35.78$

n = 100 scores from a population with σ = 20

$s = \frac{20}{\sqrt{100}} = 2$.

This one is the correct answer.

n = 100 scores from a population with σ = 40

$s = \frac{40}{\sqrt{100}} = 4$.