Question

Ms. Lee wants to know what kinds of things her students do prepare for her tests. Ms. Lee placed the names of her students into a box. To determine who she would ask about their study habits she asked a student to draw names from the box.
a. What is the sample in this situation?

b. What is the population?

(NOT A MULTIPLE CHOICE)

Answer 1

Answers:

• a) The sample is the set of students Ms. Lee selects from the box.
• b) The population is the set of all students in Ms. Lee's classroom.

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Explanation:

The first sentence tells us what the population is: it's the set of all her students. She's not concerned with any other students in any other classroom. So her "universe", so to speak, is solely focused on this classroom only. Once the population is set up, a sample of it would be a subset of the population.

If set A is a subset of set B, then everything in A is also in B, but not vice versa. For example, the set of humans is a subset of the set of mammals because all humans are mammals. However, a dog is a mammal but not a human. This shows that A is a subset of B, but not the other way around. In this example, A = humans and B = mammals.

Going back to the classroom problem, we have A = sample and B = population. If Ms. Lee has 30 students, and she randomly selects 5 of them, then those 30 students make up set B and the 5 selected make up set A. Selecting the names randomly should generate an unbiased sample. This sample should represent the population overall. If the population is small enough, the teacher could do a census and not need a sample. Though there may be scenarios that it's still effective to draw a sample.