Q. 7.25 - Elementary Statistics

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?

Step-by-Step Solution

Answer

Part a. There are N possible samples.

Part b. The possible sample means and the possible observations of the variable under consideration are the same.

Part c. There is no difference between taking a random sample of size 1 from a population and selecting a member at random from the population.

Part (a) Step 1. Given Information

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

We need to find the number of possible samples.

Part (a) Step 2. Explanation

The population size is N. And the sample size is 1.

So, there will N possible samples as each of the N population units can be a random sample.

Part (b) Step 1. Given Information

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

We need to identify the relationship between the possible sample means and the possible observations of the variable under consideration. 

Part (b) Step 2. Explanation

The mean of a single value is equal to the value itself. So the sample mean of the sample of size 1 is equal to the sample observation.

Therefore, the possible sample means and the possible observations of the variable under consideration are the same. 

Part (c) Step 1. Given Information

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

We need to identify 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

The sample mean of a random sample of size 1 is equal to the only sample observation selected from the sample.

So there is no difference between taking a random sample of size 1 from a population and selecting a member at random from the population.