Question

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Short answer

The statement made by the student is Yes, correct

Step-by-step solution

Given information 

The student made a statement "The variability of the sampling distribution of the sample mean diminishes as you take more and larger samples from a population."

Explanation 

If the sample size is higher than or equal to 30, the sampling distribution of the sample mean will be nearly normal with mean and standard deviation, according to the central limit theorem is $\sigma /\sqrt{n}$.

The standard deviation of the sampling distribution drops as the value of n increases, and the spread of the sampling distribution of the sample mean decreases.