Which statement correctly describes sampling with replacement?

Which statement correctly describes sampling with replacement?

• A. It requires sampling without replacement.
• B. It reduces the probability of selecting any given item over time.
• C. It guarantees independent draws with decreasing variance.
• D. It allows repeated draws and the population size remains the same.

Answer: (D)

Sampling with replacement means you put each item back after you draw it, so every draw starts from the full population again. Because you’re restoring the population after each draw, the chance of picking any particular item stays the same for every draw, and you can pick the same item more than once. That combination—repeated draws being allowed and the population size staying constant after each draw—is exactly what this statement conveys. The other descriptions don’t fit. Sampling without replacement would remove the item from the population after it’s drawn, so repeats aren’t possible and the population size would shrink. Saying the probability of selecting any item decreases over time is not true when you replace items—the probabilities stay constant. The note about independent draws is true in spirit, but the phrase about decreasing variance isn’t a defining feature of sampling with replacement and can be misleading without specifying what variance is being referred to.

Sampling with replacement means you put each item back after you draw it, so every draw starts from the full population again. Because you’re restoring the population after each draw, the chance of picking any particular item stays the same for every draw, and you can pick the same item more than once. That combination—repeated draws being allowed and the population size staying constant after each draw—is exactly what this statement conveys.

The other descriptions don’t fit. Sampling without replacement would remove the item from the population after it’s drawn, so repeats aren’t possible and the population size would shrink. Saying the probability of selecting any item decreases over time is not true when you replace items—the probabilities stay constant. The note about independent draws is true in spirit, but the phrase about decreasing variance isn’t a defining feature of sampling with replacement and can be misleading without specifying what variance is being referred to.