Which of the following samples is most likely to fairly represent the population when estimating a sample proportion $p$?

• A. A sample consisting only of volunteers from the population
• B. A simple random sample where every member of the population has an equal chance of being selected
• C. A sample where members are chosen based on convenience
• D. A sample taken from a single subgroup within the population

Answer: (B)

Verified step by step guidance

1. Understand that when estimating a sample proportion, the goal is to have a sample that fairly represents the entire population without bias.
2. Recognize that a simple random sample (SRS) means every member of the population has an equal chance of being selected, which helps ensure the sample is representative.
3. Identify that samples consisting only of volunteers, convenience samples, or samples from a single subgroup can introduce bias because they do not give all population members an equal chance of selection.
4. Recall that bias in sampling leads to inaccurate estimates of the population proportion because certain groups may be over- or under-represented.
5. Conclude that the sample most likely to fairly represent the population is the simple random sample, as it minimizes bias and allows for valid inference about the population proportion.