What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?
A) The underlying population must be normally distributed.
B) The underlying population must be normally distributed if the sample size is 30 or more.
C) The underlying population need not be normally distributed if the sample size is 30 or more.
D) The underlying population need not be normally distributed if the population standard deviation is known.

Question

Quizplus · Accepted Answer

The central limit theorem states that as sample size increases, the sample mean will approach a normal distribution (regardless of the underlying population distribution) with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, if the sample size is large enough (usually considered to be 30 or more), the underlying population need not be normally distributed. The population standard deviation does not affect the use of the central limit theorem.

What Conditions Are Required by the Central Limit Theorem Before