Question

Which of the following statements is NOT part of the central limit theorem?

1) The mean of the sampling distribution of the mean is equal to the population mean.
2) The variance of the sampling distribution is inversely proportional to the sample size.
3) The mean of the sampling distribution of the mean is equal to the population mean divided by the square root of the sample size.
4) The variance of the sampling distribution of the mean is equal to the population variance divided by the sample size.

Answer 1

The mean of the sampling distribution of the mean is equal to the population mean divided by the square root of the sample size.

Step-by-step explanation:

The correct answer is option (3) - The mean of the sampling distribution of the mean is equal to the population mean divided by the square root of the sample size.

The central limit theorem states that if the sample size is sufficiently large, the distribution of the sample means will be approximately normal. It also states that the mean of the sampling distribution of the mean is equal to the population mean, not divided by the square root of the sample size. Option (3) contradicts the central limit theorem, making it the correct answer.

On the other hand, options (1), (2), and (4) are correct statements that align with the central limit theorem.