Which of the following statements about the Central Limit Theorem is true?
A) The Central Limit Theorem states that the sample mean is always equal to the population mean μ.
B) The Central Limit Theorem states that the sampling distribution of the population mean μ is approximately normal provided that n ≥ 30.
C) The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n ≥ 30).
D) The Central Limit Theorem states that the sample mean is equal to the population mean μ provided that n ≥ 30.

Question

Which of the following statements about the Central Limit Theorem is true?
A) The Central Limit Theorem states that the sample mean is always equal to the population mean μ. 
B) The Central Limit Theorem states that the sampling distribution of the population mean μ is approximately normal provided that n ≥ 30. 
C) The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n ≥ 30). 
D) The Central Limit Theorem states that the sample mean is equal to the population mean μ provided that n ≥ 30.

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n ≥ 30). This means that as the sample size increases, the distribution of sample means becomes more and more normal, regardless of the shape of the population distribution. The theorem does not state that the sample mean is always equal to the population mean or that the population mean distribution is always normal.

Which of the Following Statements About the Central Limit Theorem