Which of the following best describes the relationship between a sample and a population in the context of the sampling distribution of the sample proportion $p^$?

• A. A sample includes every member of the population, so the sample proportion $p^$ always equals the population proportion $p$.
• B. A sample is unrelated to the population and is used only for descriptive statistics.
• C. A sample is a subset of the population, and the sample proportion $p^$ is used to estimate the population proportion $p$.
• D. A sample is larger than the population and provides more accurate results than the population proportion $p$.

Answer: (C)

Verified step by step guidance

1. Understand the definitions: A population is the entire group of individuals or items that you want to study, while a sample is a subset of that population selected for analysis.
2. Recognize that the sample proportion is a statistic calculated from the sample data, which serves as an estimate of the population proportion, a parameter describing the whole population.
3. Recall that the sampling distribution of the sample proportion describes the distribution of sample proportions obtained from all possible samples of the same size drawn from the population.
4. Note that the sample proportion varies from sample to sample, but on average, it tends to be close to the population proportion, making it a useful estimator.
5. Conclude that the correct relationship is that a sample is a subset of the population, and the sample proportion is used to estimate the population proportion.