In their book Freakonomics, Levitt and Dubner (2009) describe alleged cheating among teachers in the Chicago public school system. Certain classrooms had suspiciously strong performances on standardized tests that often mysteriously declined the following year when a new teacher taught the same students. In about 5% of classrooms studied, Levitt and other researchers found blocks of correct answers, among most students, for the last few questions, an indication that the teacher had changed responses to difficult questions for most students. Let’s assume cheating in a given classroom if the overall standardized test score for the class showed a surprising change from one year to the next. 

a. How are the researchers operationalizing the variable of cheating in this study? Is this a nominal, ordinal, or scale variable? 

b. Explain how researchers can use the z distribution to catch cheating teachers. 

c. How might a histogram or frequency polygon be useful to researchers who are trying to catch cheating teachers? 

d. If researchers falsely conclude that teachers are cheating, what kind of error would they be committing? Explain.