In statistics, why is a $\mathrm{sample}$ used more often than a $\mathrm{population}$ when conducting probability studies?

• A. Because probability theory only applies to $\mathrm{samples}$, not $\mathrm{populations}$.
• B. Because $\mathrm{populations}$ do not contain enough data for meaningful analysis.
• C. Because studying the entire $\mathrm{population}$ is often impractical or impossible due to time, cost, or accessibility constraints.
• D. Because $\mathrm{samples}$ always provide more accurate results than $\mathrm{populations}$.

Answer: (C)

Verified step by step guidance

1. Understand the difference between a population and a sample: A population includes all members of a defined group, while a sample is a subset of that population.
2. Recognize that studying an entire population can be very time-consuming, expensive, or even impossible, especially if the population is very large or difficult to access.
3. Know that probability theory applies to both populations and samples, but samples are used to make inferences about the population when studying the whole population is not feasible.
4. Realize that samples are selected carefully to represent the population well, allowing statisticians to estimate population parameters without examining every individual.
5. Conclude that the main reason samples are used more often than populations in probability studies is due to practical constraints like time, cost, and accessibility, not because probability theory excludes populations or because samples are inherently more accurate.