Question

Which of the following is true about the sampling distribution of the sample​ mean?

A.The standard deviation of the sampling distribution is always

sigmaσ.

B.The shape of the sampling distribution is always approximately normal.

C.The mean of the sampling distribution is always

muμ.

D.All of the above are true.

Answer 1

Answer:

C.The mean of the sampling distribution is always

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size, of at least 30, can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$.

So

A is wrong, because it is $\frac{\sigma}{\sqrt{n}}$

B is wrong, you need a sample size of at least 30.

So the correct answer is:

C.The mean of the sampling distribution is always

Answer 2

The true statement about the sampling distribution is the mean of the sampling distribution is always μ.

The sample mean of a distribution is an estimate of the population mean of the distribution.

This means that the value of the sample mean and the population mean are equal.

So, we have:

$\bar x = \mu$

The shapes of the distribution is not always normal, and the standard deviation is not always $\sigma$

Hence, the mean of the sampling distribution is always μ.

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