Question

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

What must be true regarding the distribution of the​ population?

A. Since the sample size is large enough comma the population distribution does not nbsp need to be normal.
B. The population must be normally distributed and the sample size must be large.
C. The population must be normally distributed.
D. There are no requirements on the shape of the distribution of the population.

Answer 1

C. The population must be normally distributed.

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 = (\sigma)/(√(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.