Question Video: Determining If a Given Sample Is a Simple Random Sample Mathematics • First Year of Preparatory School

Video Transcript

Suppose your school has 500 students and you need to conduct a short survey on the quality of the food served in the cafeteria. You decide that a sample of 10 students would be sufficient for your purposes. So you choose 10 students by assigning them each a number and then using the random button on your calculator to choose 10 students randomly out of the 500 and conduct the survey on them. Is that considered a simple random sample?

Remember, a simple random sample is a nonempty subset of the population where every member has an equal chance of being in that subset. In this case, we want to choose 10 students from 500. So, at first glance, it does look like we have a simple random sample. But let’s check that this selection is indeed random.

In fact, the word “random” is in the wording of the question. We’re told that each person is assigned a number, and then the random number button on a calculator is used. In this method, any two students will have the same probability of being chosen. So the correct answer is yes. This is indeed considered a simple random sample.