A large university offers undergraduate courses both in-person on its campus and digitally through an online platform. The administration of the university wishes to gauge their students’ opinions about the quality of teaching at the university; specifically, they want to estimate the proportion of all students who would agree that they are receiving good instruction. They are considering several methods for collecting this data.
a. One method they are considering is conducting a simple random sample. The university has 30,000 students, and the administrators wish to ask a sample of 500 students for their opinion of the quality of teaching. Describe a procedure for how the administrators could conduct a simple random sample in this situation.
b. A faculty member of the statistics department suggests to the administrators that they may want to consider a stratified random sample, using the primary type of instruction a student receives (in-person or digitally) as a variable for stratification. Describe in the context of the scenario why a stratified random sample may provide a more precise estimate of the proportion of all students who would agree that they are receiving good instruction than the simple random sampling method you detailed in part (a).