A Guide to Business Statistics

Chapter 8Hypothesis Tests of a Population Mean

In 2010, a business professor at the University of Central Florida confronted the students in his strategic management course about cheating on a mid-term exam.¹ The class was huge, with over 600 students. The professor was convinced that roughly 200 students had cheated by getting the answers to the exam in advance. The interesting part is that he had no direct evidence. The exams were proctored in a laboratory environment and not a single student was actively caught cheating. Rather, the professor relied on statistics to drive his initial suspicion. The professor had been teaching the class for many semesters and as part of the discovery process, he conducted hypothesis tests to compare that semester's exam grades with the historic grades from past semesters. He found a significant difference. The difference was so significant that he was confident that the abnormally high grades were not due to random chance. Rather, the difference in exam grades was large enough to strongly suspect foul play. His suspicions were later confirmed by a student who tipped the professor off about students accessing the exam questions online. The guilty students eventually admitted to cheating and the entire class was required to take a new exam. While statistical analysis was not the only thing used to confirm the suspicion of cheating, the results of hypothesis testing triggered further inquiry.

The real power of statistics is being able to use ...