Question

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

Answer 1

Answer:

Correct option: D

Step-by-step explanation:

The distribution of sample means ($\bar x$), 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,

$\mu_{\bar x}=\mu$

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

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

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).