Suppose a college has asked you to conduct a survey to determine the percentage of 8:00 AM classrooms that were full on a given morning. The college has three classroom buildings, each containing two lecture halls. Each lecture hall has a capacity of 100 students. You randomly choose one of three buildings, and stand outside the entrance when classes let out. You ask the first 60 students leaving the building how full their class was. However, you soon realize that this sample is not random because you only went to only one of the buildings and the classes at that building may not be representative of all 8:00 AM classes. Moreover, since the students you surveyed were the first to exit the building, it’s also quite possible that they all came from the same class! Realizing that your survey approach would not produce a random and representative sample, you gather some friends to help sample. You place one surveyor outside each building. You each randomly select 20 students leaving the buildings that morning and tally the results: 5 people decline to participate, 35 tell you that their class was full, and 20 tell you that their class was not full. Is your sample now representative of all classes that morning?
This question is a bit tricky. This sample still may not be representative of all classes because there is a bias in the approach. When you sample students leaving each of the buildings, you will, on average, select more people from full classes, simply because there were more people in those classes. Imagine that of the 6 classes that took place that morning, 4 were full (each having 100 students) and 2 had only 40 students each. In this case, most of the students, 400 of the total 480, were in full classes. Your sample would include more students from the full classes and therefore is not representative of all classes that took place that morning.
Based on what we have learned, how can we ensure that we choose a sample of students that is representative of all 8:00 AM classes that take place on a given morning?