Question

A sample consists of:
1. All units of the population
2. 5% units of the population
3. 12.5% units of the population
4. Any fraction of the population

• A. All units of the population
• B. 5% units of the population
• C. 12.5% units of the population
• D. Any fraction of the population

Hint:

Remember:
- All units \(\rightarrow\) Population.
- Subset of units \(\rightarrow\) Sample (no fixed percentage required).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question tests the basic terminologies used in sampling theory and statistical inference, specifically distinguishing between a population and a sample.

Step 2: Detailed Explanation:
Let us define the core statistical terms:
- Population: The entire collection of all possible observations, individuals, or items of interest under study. For instance, studying "all units of the population" is called a census.
- Sample: A sample is defined as a subset, portion, or representative fraction of the population selected for investigation.
- Sampling Fraction: The sample size (\( n \)) relative to the population size (\( N \)) is called the sampling fraction (\( f = n/N \)).
This fraction is not restricted to any fixed percentage like \( 5% \) or \( 12.5% \). Depending on the study design, resources, and required precision, a sample can represent any non-zero, proper fraction of the population.
Thus, any fractional subset of a population selected to infer characteristics about the entire population constitutes a sample.

Step 3: Final Answer:
A sample consists of any fraction of the population.
Therefore, the correct choice is Option (D).