Which of the following best describes the difference between random selection and nonrandom selection in probability studies?

• A. Random selection means every member of the population has an $\mathrm{equal}$ chance of being chosen, while nonrandom selection does not guarantee $\mathrm{equal}$ chances for all members.
• B. Random selection is only used when the population is very $\mathrm{small}$, while nonrandom selection is used for $\mathrm{large}$ populations.
• C. Random selection always produces the $\mathrm{same}$ sample every time, while nonrandom selection produces $\mathrm{different}$ samples.
• D. Nonrandom selection is preferred in probability studies because it reduces $\mathrm{bias}$, while random selection increases $\mathrm{bias}$.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of random selection. In probability studies, random selection means that every member of the population has an equal chance of being chosen. This ensures fairness and representativeness in the sample.
2. Step 2: Understand nonrandom selection. Nonrandom selection does not guarantee that every member of the population has an equal chance of being chosen. This can lead to bias because some members may be more likely to be selected than others.
3. Step 3: Compare the implications of both methods. Random selection helps to reduce bias and allows for generalization of results to the entire population, while nonrandom selection can introduce bias and limit the validity of conclusions.
4. Step 4: Evaluate the given answer choices by matching them against the definitions and implications of random and nonrandom selection.
5. Step 5: Identify the correct description as the one stating that random selection means every member has an equal chance of being chosen, while nonrandom selection does not guarantee equal chances for all members.