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.

Question

Cory Miranda

Mathematics

27 November, 16:45

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.

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Answers (1)

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Robert Yang · Answer 1

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

Step-by-step 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.