Final answer:
The true statement about a perfectly random sample is that it provides every member of the population with an equal chance of being selected, which is vital for accurate representation and generalization. The correct option is B.
Step-by-step explanation:
Which of the following is true of a perfectly random sample? The correct answer is b. It provides every member of the population with an equal chance of being selected. This aspect of randomness in sampling is crucial because it ensures that the sample represents the population as accurately as possible, allowing for reliable generalizations.
Random sampling methods like simple random sampling, stratified sampling, and cluster sampling aim to achieve this representation by giving each individual an equal likelihood of selection, counteracting potential biases that might otherwise skew the results.
Gathering information about an entire population is often impractical, which is why samples are used as a representation of that population. Convenience sampling is a nonrandom method and often introduces bias to the data, whereas random sampling strives to mirror the population's characteristics as closely as possible.