Which of the following statements about the sampling distribution of the sample mean is incorrect?
A) The mean of the sampling distribution is $\mu$.
B) The sampling distribution is generated by repeatedly taking samples of size $n$ and computing the sample means.
C) The standard deviation of the sampling distribution is $\sigma$.
D) The sampling distribution is approximately normal whenever the sample size is sufficiently large $( n \geq 30 )$.

Question

Which of the following statements about the sampling distribution of the sample mean is incorrect? 
A) The mean of the sampling distribution is $\mu$.
B) The sampling distribution is generated by repeatedly taking samples of size $n$ and computing the sample means.
C) The standard deviation of the sampling distribution is $\sigma$.
D) The sampling distribution is approximately normal whenever the sample size is sufficiently large $( n \geq 30 )$.

Quizplus · Accepted Answer

The standard deviation of the sampling distribution, also known as the standard error, is $\sigma / \sqrt{n}$, not $\sigma$. This reflects how the variability of the sample mean decreases as the sample size increases.

Which of the Following Statements About the Sampling Distribution of the Sample