In the context of the sampling distribution of the sample proportion $p$, why is a sample typically used instead of collecting data from the entire population?

• A. Because using a sample eliminates all sampling error.
• B. Because a sample always gives the exact value of the population proportion $p$.
• C. Because collecting data from the entire population is often impractical or too costly, while a sample provides a reasonable estimate of the population proportion $p$.
• D. Because population data is always less accurate than sample data.

Answer: (C)

Verified step by step guidance

1. Understand the concept of a population proportion, which is the true proportion of a characteristic in the entire population.
2. Recognize that collecting data from the entire population (a census) can be very time-consuming, expensive, or even impossible in many real-world situations.
3. Learn that a sample is a smaller subset of the population selected to represent the whole, making data collection more practical and efficient.
4. Know that the sample proportion is used as an estimate of the population proportion, and while it may have some sampling error, it provides useful information without needing to survey everyone.
5. Realize that the sampling distribution of the sample proportion helps us understand the variability of this estimate across different samples, which is why sampling is a fundamental approach in statistics.