If the sampling distribution of the sample means approximates a normal distribution, then the population is normally distributed.

Question

Quizplus · Accepted Answer

The statement is actually the reverse of the true relationship between the population distribution and the sampling distribution. The sampling distribution of the sample means will approach a normal distribution regardless of the population distribution, as long as the sample size is sufficiently large due to the central limit theorem. Therefore, a normal sampling distribution cannot guarantee a normal population distribution.

If the Sampling Distribution of the Sample Means Approximates a Normal