Which of the following is a requirement for an independent random sample?

• A. The sample must include every member of the population.
• B. Each observation in the sample is selected independently of the others.
• C. The sample size must be larger than the population size.
• D. Each observation must have a different probability of being selected.

Answer: (B)

Verified step by step guidance

1. Understand the concept of an independent random sample: it means that each observation in the sample is chosen without influencing or depending on the selection of any other observation.
2. Recognize that independence in sampling implies that the selection of one member does not affect the probability of selecting another member.
3. Note that including every member of the population corresponds to a census, not a sample, so this is not a requirement for an independent random sample.
4. Understand that the sample size cannot be larger than the population size, so this condition is invalid for any sample.
5. Recall that in a simple random sample, each observation should have the same probability of being selected, so having different probabilities contradicts the idea of a random sample.