Question

question 8
which of the following statements about the sampling distribution of the sample mean is incorrect?
the sampling distribution is approximately normal whenever the sample size is sufficiently large (n ≥ 30).
the mean of the sampling distribution is μ.
the standard deviation of the sampling distribution is σ.
the sampling distribution is generated by repeatedly taking samples of size n and computing the sample means.
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Explanation:

The standard deviation of the sampling distribution of the sample - mean (also known as the standard error) is $\frac{\sigma}{\sqrt{n}}$, not $\sigma$ where $\sigma$ is the population standard deviation and $n$ is the sample size. The other statements are correct facts about the sampling distribution of the sample - mean. The Central Limit Theorem states that the sampling distribution is approximately normal for $n\geq30$. The mean of the sampling distribution of the sample - mean is equal to the population mean $\mu$, and the sampling distribution is generated by repeatedly taking samples of size $n$ and computing the sample means.

Answer:

The standard deviation of the sampling distribution is $\sigma$.