Question

Suppose a simple random sample of size n = 14 is obtained from a population with μ = 61 and σ = 17.

Answer 1

Answer:

C. The population must be normally distributed.

Step-by-step explanation:

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For us to apply the central limit theorem with a sample size of 14, the underlying population must be normally distributed.

So the correct answer is:

C. The population must be normally distributed.