In the context of the sampling distribution of sample proportion, what does it mean when a part of the population is under-represented in a sample?

• A. The sample size is always larger than the population size, causing overestimation of the population proportion.
• B. Every group in the population is equally likely to be included in the sample, ensuring an unbiased estimate.
• C. The sample proportion will always be exactly equal to the population proportion.
• D. Some groups in the population have a lower chance of being included in the sample, which can lead to biased estimates of the population proportion.

Answer: (D)

Verified step by step guidance

1. Understand that the sampling distribution of the sample proportion describes how the proportion calculated from different samples varies around the true population proportion.
2. Recognize that when a part of the population is under-represented in a sample, it means that some groups have a lower probability of being selected compared to others.
3. This unequal chance of selection causes the sample to not accurately reflect the population's true composition, leading to biased estimates of the population proportion.
4. Recall that for an unbiased estimate, every member or group in the population should have an equal chance of being included in the sample, ensuring the sample proportion is a good estimator of the population proportion.
5. Therefore, under-representation violates this principle and affects the validity of conclusions drawn from the sample proportion about the population.