Why is a $\mathrm{sample}$ used more often than a $\mathrm{population}$ when studying the sampling distribution of the $\mathrm{sample} \mathrm{proportion}$?

• A. Because the $\mathrm{population}$ is usually too small to provide meaningful results.
• B. Because collecting data from an entire $\mathrm{population}$ is often impractical or too costly, so a $\mathrm{sample}$ provides a manageable and efficient way to estimate $\mathrm{population} \mathrm{parameters}$.
• C. Because using a $\mathrm{sample}$ eliminates all sources of bias in statistical analysis.
• D. Because a $\mathrm{sample}$ always gives more accurate results than using the entire $\mathrm{population}$.

Answer: (B)

Verified step by step guidance

1. Understand the difference between a population and a sample: A population includes all members of a group being studied, while a sample is a subset of that population.
2. Recognize that studying the sampling distribution of the sample proportion involves analyzing how the proportion varies across different samples drawn from the population.
3. Consider practical constraints: Collecting data from an entire population is often impractical due to time, cost, and resource limitations.
4. Note that using a sample allows statisticians to make inferences about the population proportion without needing to survey everyone, making the process more efficient and manageable.
5. Remember that while samples can introduce sampling variability, proper sampling methods help ensure that the sample proportion is a good estimator of the population proportion.