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 spread of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Answer 1

No, the student is not right as his statement is against central limit theorem.

Explanation:

Central Limit Theorem:

This theorem states that if we take large samples of a population which has a mean and standard deviation then mean samples will have a normal distribution.

• So the statement of this theorem negates the statement of the boy who said that the spread of sampling distribution of the sample mean will decrease.