An administrator at a university with an average enrollment of 25,000 students wants to estimate the number of students who had cheated on a major exam during the past semester. How many students would need to be included in a random sample of students if you want to be 95% confident that your sample estimator is within 2 percentage points of the proportion for the whole campus? Calculate the sample size under each of the following assumptions.
a. Previous studies at other universities had determined π to be less than 20%.
b. You think that the students at your university have higher ethical standards than students at most other universities.
c. You have no idea what the value of π would be at your university compared to the other universities.