Which of the following best describes the relationship between a $\mathrm{sample}$ and a $\mathrm{population}$ in the context of the sampling distribution of the sample proportion?

• A. A $\mathrm{sample}$ is always larger than the $\mathrm{population}$.
• B. A $\mathrm{sample}$ is a subset of the $\mathrm{population}$ used to estimate characteristics of the entire $\mathrm{population}$.
• C. A $\mathrm{sample}$ and a $\mathrm{population}$ are always the same group.
• D. A $\mathrm{sample}$ includes every member of the $\mathrm{population}$.

Answer: (B)

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 smaller group selected from the population.
2. Recognize that the sample is used to make inferences or estimates about the population, especially when it is impractical to study the whole population.
3. Recall that the sample proportion is a statistic calculated from the sample data, which serves as an estimate of the population proportion, a parameter.
4. Note that the sampling distribution of the sample proportion describes the distribution of this statistic over many possible samples drawn from the population.
5. Conclude that the sample must be a subset of the population, not larger or identical to it, and it does not include every member of the population.