Q.7.24 - Elementary Statistics

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

Step-by-Step Solution

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.

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.