The Central Limit Theorem is important in statistics because
A) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
B) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
C) for a large n, it says the population is approximately normal.
D) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that for a large sample size (n), the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. This is important in statistics because it allows us to make inferences about population parameters using sample means and gives us a way to estimate the uncertainty in those estimates. Option A is incorrect because the Central Limit Theorem only applies to the sampling distribution of the sample mean, not any other sampling distribution. Option C is incorrect because the Central Limit Theorem does not make any assumptions about the population being normal. Option D is incorrect because the Central Limit Theorem only applies when n is large.

The Central Limit Theorem Is Important in Statistics Because