If the sample size is much smaller than the population size, say 20 times smaller, then random sampling with replacement and random sampling without replacement are nearly equivalent. True / False.

Question

Delaney Weber

Mathematics

12 November, 19:31

If the sample size is much smaller than the population size, say 20 times smaller, then random sampling with replacement and random sampling without replacement are nearly equivalent. True / False.

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Addison Archer · Answer 1

True

Step-by-step explanation:

If the sample size is smaller enough to make make the population size infinite i. e. 20 times larger then the sample size then the co-variance (a property of retaining the original form of a function when variables are transformed linearly) becomes nearly equal to zero. In this way sampling with replacement (large population) is not different from the sampling without replacement (small and finite population) as co-variance is close to zero. Thus they are nearly equal.

For example:

The simple sampling with replacement is that every individual has the same probability of being chosen i. e. for a small sample from a large population, while sampling without replacement is approximately the same, since the chances of choosing the same individual is low.