Which of the following is NOT a property of the sampling distribution of the sample mean?

Choose the correct answer below.

A.

The sample means target the value of the population mean.

B.

The mean of the sample means is the population mean.

C.

The expected value of the sample mean is equal to the population mean.

D.

The distribution of the sample mean tends to be skewed to the right or lef

The distribution of sample means ([tex]\bar x[/tex]), computed from various samples drawn from the same population, is known as the sampling distribution of sample means.

According to the Central Limit Theorem, if we have a population with mean μ and standard deviation σ and a huge random-samples (n ≥ 30) from the population is selected with replacement, then the distribution of the sample means will be approximately Normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means (also known as the standard error)is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The probability curve for the sampling distribution of sample mean is symmetric and bell-shaped.

Thus, the statement that is not a property of the sampling distribution of the sample mean is (D).