• Understand the difference between sampling with and without replacement

Sampling With and Without Replacement

The usual way to select a random sample from a population is using sampling without replacement. This means that once an individual from the population is selected for the sample and data are recorded for that individual, they are not considered again when making additional selections from the population for that sample. In sampling without replacement, no individual is included in the sample more than once. 

Sampling with replacement is different in that after an individual is selected for the sample and data are recorded for that individual, they are “replaced” (put back into the population) before the next selection is made. This means that it is possible that the same individual might be selected again, and their data would then be included more than once in the sample.

Francisco lives in a college dorm that encourages students to engage in community service. Francisco plans to take a sample of [latex]20[/latex] students from the [latex]200[/latex] students living in his dorm to learn about the average number of hours per month spent doing community service. Here is how he plans to select his sample:

• Obtain a list of the [latex]200[/latex] students who live in the dorm.
• Number the students on the list from [latex]1[/latex] to [latex]200[/latex].
• Use a random number generator to obtain [latex]20[/latex] random numbers between [latex]1[/latex] and [latex]200[/latex]. If any numbers are repeated in the list of [latex]20[/latex] random numbers, he will ignore the repeats and generate additional random numbers until he has [latex]20[/latex] numbers that are all different.
• Create a list of [latex]20[/latex] students by using the random numbers to identify which students on his numbered list of [latex]200[/latex] students will be included in the sample.
• Contact each of the students selected for the sample and record the number of hours per month that they report spending doing community service.