Question

Suppose that a random sample of size $1$is to be taken from a finite population of size $N$.

a. How many possible samples are there?

b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.

c. What is the difference between taking a random sample of size $1$from a population and selecting a member at random from the population?

Short answer

(a) Because each of the population's $N$units might be a random sample, there are $N$possible samples.

(b) The sample means are exactly equivalent to the variable under consideration's possible observation.

(c) There is no change because the sample mean of a random sample of size is equal to the sample's single sample observation.

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that sample of size $1$is to be taken from a finite population of size $N$we have to find the total possible samples are there.

Part (a) Step 2: Explanation 

We have to draw a random sample of size $1$from the population.

Because each of the $N$population units can be a random sample, there are $N$possible samples.

Part (b) Step 1: Given Information 

Given in the question that sample of size $1$is to be taken from a finite population of size $N$we have to find the relationship between the possible sample means and the possible observations of the variable under consideration.

Part (b) Step 2: Explanation 

Nothing except the sample observation since mean of a single value to that value in a sample of size $1$.

therefore, The sample means are exactly equivalent to the variable under consideration's possible observation.

Part (c) Step 1: Given Information 

Given in the question that sample of size $1$is to be taken from a finite population of size $N$ we have to find the difference between taking a random sample of size $1$ from a population and selecting a member at random from the population.

Part (c) Step 2: Explanation 

There is no change because the sample mean of a random sample of size is equal to the sample's single sample observation.