Answer to Question #175088 in Statistics and Probability for Reive Lawrenz Labiaga

Question

Which of the following is false about the central limit theorem (CLT)?

a.As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

b.If we take more samples from the original population, the sampling distribution is more likely to be nearly normal.

c.The CLT states that the sampling distribution will be centered at the true population parameter.

d.If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size.

Answer 1

Solution:

A. It is true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. 

B. It is true. The CLT states that the sampling distribution will be centered at the true population parameter. 

C. It is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. 

D. It is false.

The correct statement is:

The central limit theorem states that if you have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. 

Thus, D is false.