Chapter 7.1, Problem 1E

To determine

To State:

Whether the given statement is true or false.

Answer to Problem 1E

Solution:

The statement “A sampling distribution refers to individuals rather than groups” is false.

Explanation of Solution

Given:

The given statement “A sampling distribution refers to individuals rather than groups.”

Description:

Given a population of size $N$ with mean $\left(\mu \right)$ and standard deviation $\left(\sigma \right)$, samples of a fixed discrete number of trials $\left(n\right)$ can be chosen each having a mean called the sample mean $\left(\overline{x}\right)$.

On dealing with the collection of these means for samples chosen from the population, the concept of sampling distribution pops and the statistic dealt with is the sample mean, and that the distribution contains all possible samples for the chosen sample size.

The continuity criterion can be extended and here it is known as Central Limit Theorem which states that sampling distribution is approximately normal.

Now,

The sampling distribution deals with samples of a fixed size which are not individuals but groups.

Conclusion:

The statement “A sampling distribution refers to individuals rather than groups” is false. On the contrary, the sampling distribution refers to groups taking into consideration the distribution of their means.