Question

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is Select one: a. less than 2 b. 2 c. greater than 2 d. 3

Answer 1

Answer:

b. 2

Step-by-step explanation:

The Central Limit Theorem is important to solve this question.

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

In this problem, we have that:

$\sigma = 14, n = 49$

The standard error of the mean is

$\frac{14}{\sqrt{49}} = 2$

So the correct answer is:

b. 2