In the context of sampling distributions of sample proportions, $\mathrm{population}\mathrm{parameters}$ are difficult to calculate due to which of the following reasons?

• A. $\mathrm{Population}\mathrm{parameters}$ are always equal to $0$.
• B. It is often impractical or impossible to collect data from every member of the $\mathrm{population}$.
• C. $\mathrm{Sampling}\mathrm{distributions}$ do not require knowledge of the $\mathrm{population}$.
• D. $\mathrm{Sample}\mathrm{statistics}$ always exactly match $\mathrm{population}\mathrm{parameters}$.

Answer: (B)

Verified step by step guidance

1. Understand that population parameters refer to values that describe characteristics of an entire population, such as the true population proportion \(p\).
2. Recognize that calculating these parameters directly requires data from every member of the population, which is often very large or inaccessible.
3. Realize that because collecting data from every individual is usually impractical or impossible, we rely on samples to estimate these parameters.
4. Know that sample statistics, like the sample proportion \(\hat{p}\), are used to approximate population parameters, and their distribution across samples is described by the sampling distribution.
5. Therefore, the difficulty in calculating population parameters arises primarily because it is often impractical or impossible to collect data from every member of the population.