Why is a sample used more often than a population when studying the sampling distribution of the sample proportion $p^$?

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

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 entire population is often impractical due to constraints such as time, cost, and accessibility.
3. Know that a sample allows us to estimate population parameters without needing to collect data from every individual, making the process more efficient.
4. Learn that the sampling distribution of the sample proportion is based on repeated samples, which helps us understand the variability and reliability of the sample proportion as an estimator.
5. Conclude that using a sample is a practical approach to infer about the population, balancing accuracy and feasibility, rather than always aiming for complete population data.