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Chapter 7: Problem 15

Explain the difference between sampling with replacement and sampling without replacement. Suppose you have the names of 10 students, each written on a 3 -inch by 5 -inch notecard, and want to select two names. Describe both procedures.

Short Answer

Expert verified
Sampling with replacement means that after a sample is selected, it's returned back to the population and could be selected again. Sampling without replacement means the selected sample is not returned back to the population and therefore can't be chosen again. In the exercise, sampling with replacement could lead to the same student's name being picked twice, while sampling without replacement guarantees two different students' names will be picked.

Step by step solution

01

Define Sampling With Replacement

When sampling with replacement, an individual from the population is selected at random for inclusion in the sample. After being selected, it's 'replaced' back into the population and could potentially be chosen again.
02

Define Sampling Without Replacement

In contrast, when sampling without replacement, an individual chosen for the sample is not returned to the population, so cannot be chosen again. This can alter the probability of future individuals being selected.
03

Apply The Concepts To The Exercise

If given 10 notecards each with a student's name (assume they are all different), and selecting two names: \n\n1) Using sampling with replacement: The first card is picked, observed, then returned to the pool. The second card is then selected from the full set of 10 again. Therefore, it's possible for the same card (i.e., the same student) to be selected twice.\n\n 2) Using sampling without replacement: The first card is similarly picked and observed but NOT returned to the pool. When the second card is picked, it's picked from the remaining 9 cards. As such, it's impossible for the same name to be selected twice.

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