Question

Mateo teaches a continuing education class at the library on Tuesday nights. He estimates that 75% of his students are satisfied or very satisfied with the class.

Last week, he asked a random sample of students to take a survey on their experience in the class. However, the results showed that only 70% indicated that they are satisfied or very satisfied with the class. He decides to randomly survey more of his students. How will Mateo know whether his model is valid or not?

A.
It is valid if the result from all the surveys and the model get farther apart.
B.
It is valid if the result from all the surveys and the model get closer together.
C.
It is valid if the result from all the surveys and the model stay the same.
D.
It is impossible to determine whether the model is valid.

Answer 1

@BYEWORLD

Answer 2

So he used some kind of statistical model to estimate that 75% of his students are satisfied with the class.

The purpose of a (good) statistical model is to accurately represent data. If his model is good, then the number of students who actually are satisfied with his class should be close to 75%.

He took a random sample and got 70%. If he keeps surveying students *and* his model is good, then we would expect to get closer and closer results to his model (75%). If the actual number gets farther and farther away from his model, then it’s probably not a good/valid model.

Therefore, his model is valid if result from all the surveys and the model get closer together.