Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal.
A)It has the same shape,mean and standard deviation as the population.
B)It has the same mean as the population,but a different shape and standard deviation.
C)It the same mean and standard deviation as the population,but a different shape.
D)It has the same shape and mean as the population,but a different standard deviation.

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the mean for a large sample size (>30) will approach a normal distribution regardless of the shape of the population distribution. However, the mean of this sampling distribution will be equal to the mean of the population. The standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. Therefore, the shape and standard deviation of the sampling distribution will be different from the population, but the mean will be the same. Choice B correctly reflects this.

Which of the Following Is True Regarding the Sampling Distribution