Question

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.

Answer 1

Answer:

No. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample's mean.                  

Explanation:

Central limit theorem: In statistics, the term "central limit theorem" is defined as the phenomenon which describes that if an individual or researcher consists of a specific population having a mean "μ" and therefore standard deviation as "σ" and then thereafter he or she takes significantly large samples from a particular population with replacement then it would be considered that the distribution of the given sample means is supposed to be normally distributed.

In the question above, the student is not right as the central limit theorem doesn't explain anything about the histogram of given sample values.