Which of the following is true regarding the sampling distribution of the mean for a large sample size?
A) It has a normal distribution with the same mean and standard deviation as the population.
B) It has a normal distribution with the same mean as the population but with a smaller standard deviation.
C) It has the same shape, mean, and standard deviation as the population.
D) It has the same shape and mean as the population, but has a smaller standard deviation.

Question

Quizplus · Accepted Answer

The sampling distribution of the mean for a large sample size (according to the Central Limit Theorem) will have a normal distribution with the same mean as the population from which the samples are drawn. However, the standard deviation of the sampling distribution (often called the standard error) will be smaller than the standard deviation of the population, decreasing with the square root of the sample size.

Which of the Following Is True Regarding the Sampling Distribution