Which of the following statements is true regarding the sampling distribution of means?
A) If the population from which a sample was drawn is not normal, then the sampling distribution cannot be normal.
B) If the sample drawn from the population is small enough, then the sampling distribution can be normal, even if the population itself is not.
C) If the sample drawn from the population is large enough, then the sampling distribution can be normal, even if the population itself is not.
D) None of the above statements is true.

Question

Quizplus · Accepted Answer

The central limit theorem states that if the sample size is large enough (usually N > 30) then the distribution of sample means will be approximately normal regardless of the population distribution. Therefore, option C is correct. Option A is incorrect because the central limit theorem does not depend on the population being normal. Option B is incorrect because a small sample size does not guarantee a normal sampling distribution.

Which of the Following Statements Is True Regarding the Sampling