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

• A. Because using a $\mathrm{sample}$ eliminates all sampling error.
• B. Because $\mathrm{populations}$ do not have proportions.
• C. Because it is usually impractical or impossible to collect data from the entire $\mathrm{population}$.
• 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 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 from sample to sample, not from the entire population directly.
3. Consider the practical challenges: Collecting data from an entire population is often impractical or impossible due to constraints like time, cost, and accessibility.
4. Note that samples allow statisticians to make inferences about the population proportion without needing to measure every individual, which is why samples are used more often.
5. Remember that using a sample does not eliminate sampling error; instead, it provides a manageable way to estimate population parameters and understand variability through the sampling distribution.