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.
Central limit theorem deals with distribution of the mean of sample.
the sample means distribution approximates to a normal distribution when the size of the sample becomes larger, regardless of the population's distribution.
Thus, the student is wrong as the CLT does not say anything about given sample's histogram values.
