Which of the following statements is true? 1. The Central Limit Theorem states t

Question

Which of the following statements is true?

1. The Central Limit Theorem states that a sampling distribution will not have the same shape as the population distribution from which it is taken.

2. The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n>1)

3. The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.

4.  None of 1 through 4 are true.

Explanation / Answer

1. The Central Limit Theorem states that a sampling distribution will not have the same shape as the population distribution from which it is taken.

This statement is not true. If the population distribution is already bell shaped, it can match the sampling distribution shape.

2. (This statement is incomplete.)

3. The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.

This statement is true and is the correct interpretation of the Central limit theorem.

The correct answer is 3.

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