Question

Suppose that a sample is to be taken without replacement from a finite population of size Nif the sample size is the same as the population size

(a) How many possible samples are there?

(b) What are the possible sample means?

(c) What is the relationship between the only possible sample and the population

Short answer

Part a. Only one possible sample is there.

Part b. There is only one possible sample mean which is equal to the population mean.

Part c. The only possible sample is the same as the population itself.

Step-by-step solution

Part (a) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find out how many possible samples are there.

Part (a) Step 2. Explanation

We have a population of size N. And we have to draw a sample of size N without replacement.

There will be only one possible sample since we are drawing the sample without replacement and the sample size is equal to the population size.

So there is only one possible sample and it is the population itself.

Part (b) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find the total possible sample means.

Part (b) Step 2. Explanation

As there is only one possible sample and it is the population itself.

So there will be only one possible sample mean and it would be equal to the population mean itself.

Part (c) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find the relationship between the only possible sample and the population.

Part (c) Step 2. Explanation

As there is only one possible sample and it is the population itself.

So the relation between the only possible sample and the population is that they are the same.