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

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

Answer: (B)

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. Learn that samples are used to make inferences about the population because they are more practical to collect and analyze within reasonable constraints.
4. Know that probability theory applies to both populations and samples, but samples are often used because they allow for manageable data collection and analysis.
5. Conclude that the main reason samples are used more often than populations in probability studies is due to practical limitations, not because samples are inherently more accurate or because populations lack data.