Which of the following is true about the sampling distribution of the sample mean?
A) The mean of the sampling distribution is always μ.
B) The standard deviation of the sampling distribution is always σ.
C) The shape of the sampling distribution is always approximately normal.
D) All of the above are true.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution is always equal to the population mean, μ.

Answer: B
 The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, σ/√n.

Answer: C
 The shape of the sampling distribution is approximately normal if the sample size is large enough (typically n ≥ 30) or if the population distribution is normal. Therefore, this statement is not always true, but is often true in practice.

Therefore, the answer is: A, B.

Which of the Following Is True About the Sampling Distribution