Question

Suppose 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

(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

(a) There can only be one possible sample, which is the population as a whole.

(b) The population mean is the only sample mean that exists.

(c) The population as a whole is the only option.

Step-by-step solution

Part (a) Step 1: Given Information

Given in the question that a sample is to be taken without replacement .

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

Part (a) Step 2: Explanation

Let's say we have a population of size $N$, and we need to draw a sample of size $N$with no replacements.

Because we are drawing sample units without replacement and the sample size is equal to the population size, there will be just one sample. As a result, there can only be one possible sample, which is the entire population.

Part (b) Step 1: Given Information

Given in the question that a sample is to be taken without replacement .

we have to find the total possible sample means.

Part (b) Step 2: Explanation

Clearly, The population mean is the only sample mean that exists.

Part (c) Step 1: Given Information

Given in the question that a sample is to be taken without replacement .

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

Part (c) Step 2: Explanation

We can said that the relationship between the only possible sample and the population is The population as a whole is the only option.