Which of the following best describes the difference between a census and a sample in the context of estimating a population proportion $p$?

• A. A census and a sample both collect data from subsets of the population, but a census uses a larger subset.
• B. A census collects data from every member of the population, while a sample collects data from only a subset of the population.
• C. A census uses random selection, while a sample always includes the entire population.
• D. A census is only used when the population is very large, while a sample is used for small populations.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definitions of 'census' and 'sample' in statistics. A census involves collecting data from every member of the entire population, while a sample involves collecting data from only a part or subset of the population.
2. Step 2: Recognize that the key difference lies in the scope of data collection: a census aims for complete data coverage, whereas a sample aims for partial data coverage that represents the population.
3. Step 3: Consider the practical implications: a census is often more time-consuming and costly because it requires data from all individuals, while a sample is more efficient but requires careful selection to ensure representativeness.
4. Step 4: Evaluate the answer choices by comparing them to these definitions. The correct description should clearly state that a census collects data from every member of the population, and a sample collects data from only a subset.
5. Step 5: Conclude that the best description is the one stating: 'A census collects data from every member of the population, while a sample collects data from only a subset of the population.'