Which of the following statements about the Central Limit Theorem (CLT) is correct?
A) The CLT states that the sample mean x̄ is always equal to the population mean, μ.
B) The CLT states that the sampling distribution of the population mean μ is approximately normal, provided that n ≥ 100.
C) The CLT states that the sampling distribution of the sample mean x̄ is approximately normal for large sample sizes (n ≥ 30).
D) The CLT states that the sample mean x̄ is equal to the population mean μ , provided that n ≥ 30 .
E) The CLT states that the sampling distribution of the population mean μ is approximately normal, provided that n ≥ 30 .

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean x̄ is approximately normal for large sample sizes (n ≥ 30). The theorem does not state that the sample mean is always equal to the population mean or that the population mean sampling distribution is normal provided that n ≥ 100 or n ≥ 30.

Which of the Following Statements About the Central Limit Theorem