Discuss the below:
Q: A university's associate directors for whom a statistician was consulting were interested in alumni donations, as are many schools, not only because they want the money but also because it is one of the criteria by which U.S. News & World Report ranks U.S. institutions of higher learning. U.S. News includes this criterion because higher rates of alumni giving are seen as indicative of the satisfaction of former students. An increase in a school's overall ranking by this magazine has been demonstrated to translate into an increase in applications, and all schools want that, even though there is controversy about the validity of these rankings. One set of rankings is for the best national universities: institutions that offer undergraduate, master's, and doctoral degrees and have an emphasis on research. (Harvard tops the list that was published in 2005.) Here are the alumni giving rates that were reported in 2005; the rates are the percentages of alumni who donated to each of the top 70 national universities in the year prior to publication of these data.
48 61 45 39 46 37 38 34 33 47
29 38 38 34 29 29 36 48 27 25
15 25 14 26 33 16 33 32 25 34
26 32 11 15 25 9 25 40 12 20
32 10 24 9 16 21 12 14 18 20
18 25 18 20 23 9 16 17 19 15
14 18 16 17 20 24 25 11 16 13
a. How was the variable of alumni giving operationalized? What is another way that this variable could be operationalized?
b. Create a grouped frequency table for this data.
c. The data has quite a range, with the lowest scores belonging to Boston University, the University of California at Irvine, and the University of California at San Diego, and the highest belonging to Princeton University. What research hypotheses come to mind when you examine these data? State at least one research question that these data suggest to you.