In this election season, we use polling constantly and the folks here do a great job. They are careful and they do a good job of assessing the mathematical strengths and weaknesses of various polls. I am a former high school math teacher and my job included teaching my students about polling. Here is a polling problem I used to give to them more than 50 years ago, long before polls and computers were commonplace. So my purpose was to teach them about polls and the potentiality of computers.
A question about public opinion polling samples.
I would ask the class to solve the following problem:
Suppose you are a high school mathematics teacher and you are trying to help your students understand how public opinion polling works. Suppose you ask the class what sort of sample they would use to determine the opinion of the citizenry on a very simple question that requires a "yes" or "no" answer. Suppose you tell them that the process will work perfectly. You grant this condition because you want to them to concentrate on the math, not on extraneous issues. Suppose you say that the sample size is 435 and the population is all American citizens.
One group of the class says that they will use a perfect random selection program to select 435 people from a file of all American citizens.
A second group says that they will just call each of the 435 members of the House of Representatives and ask them the question.
A third group says that they will go to the state fair midway and ask the question to the first 435 people they meet.
Remember, no matter which sampling approach is used, the poll will work perfectly. There will be no confusion.
Now, as the teacher,you must tell them which approach will more likely reflect the opinions of the general population of all American citizens. Which one is it, number 1, 2, or 3?
This problem has real application to a very complex situation that I have frequently encountered.