Which of the following correctly describes the central limit theorem with respect to ?
A) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution as sample size, n increases.
B) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution when n30 and also n

Question

Which of the following correctly describes the central limit theorem with respect to  ?
A) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution as sample size, n increases. 
B) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution when n30 and also n < .05 N, because these values make the approximation near-perfect. 
C) Ifis the mean of a simple random sample taken from a large population and if the N population values are normally distributed, the sampling distribution ofis also normally distributed, regardless of sample size, n. 
D) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution as sample size, n increases and Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution when n30 and also n < .05 N, because these values make the approximation near-perfect. 
E) Ifis the mean of a simple random sample taken from a large population and if the N population values are not normally distributed, the sampling distribution ofnevertheless approaches a normal distribution when n30 and also n < .05 N, because these values make the approximation near-perfect and Ifis the mean of a simple random sample taken from a large population and if the N population values are normally distributed, the sampling distribution ofis also normally distributed, regardless of sample size, n.

Quizplus · Accepted Answer

This choice correctly describes the central limit theorem by stating that the sampling distribution of the sample mean approaches a normal distribution as sample size increases, even if the population values are not normally distributed. It also includes the added information that the approximation becomes near-perfect when n is greater than 30 and less than 5% of the population size. Choice B is partially correct but misses the aspect of n approaching 30 for the approximation to be near-perfect. Choice A is incorrect because it does not mention the importance of sample size, and choice C is incorrect because it only applies to normally distributed populations. Choice E includes both correct and incorrect information, with the incorrect information being that normally distributed populations always result in normal sampling distributions regardless of sample size.

Which of the Following Correctly Describes the Central Limit Theorem