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 $\mathrm{sample}$ includes every member of the $\mathrm{population}$.
• B. A $\mathrm{sample}$ is unrelated to the $\mathrm{population}$ from which it is drawn.
• C. A $\mathrm{sample}$ is a subset of the $\mathrm{population}$ used to estimate characteristics of the entire $\mathrm{population}$.
• D. A $\mathrm{sample}$ and a $\mathrm{population}$ always have the same size.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definitions of population and sample. 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. Step 2: Recognize that the sample is used to make inferences about the population because it is often impractical or impossible to study the entire population.
3. Step 3: Note that the sample must be representative of the population to provide accurate estimates of population parameters, such as the population proportion.
4. Step 4: Understand that the sampling distribution of the sample proportion describes the distribution of sample proportions obtained from all possible samples of a fixed size drawn from the population.
5. Step 5: Conclude that the correct relationship is that a sample is a subset of the population used to estimate characteristics of the entire population, which aligns with the concept of sampling distributions.