Question

2. Administrators at State University have noticed that the students who pass Math 100 in their first year have much higher graduation rates, compared to students who don't take, or fail, or drop Math 100. In particular, they find for students matriculating in 2012 Completes Doesn't Complete Math 100 240 60 Math 100 110 90 Graduate in 5 years Doesn't Graduate in 5 Graduate in 5 years Wow!" they say. "All we have to do is make it easier for students graduation rates will go up!" pass Math 100, and (a) State some formal hypotheses and obtain a p-value to verify that the difference in graduation rates is statistically significant (b) To convince the administrators of the fallacy of their thinking, you show them a possible disaggregation of the data, based on the students' math SAT scores. Fill in the blanks and compute the appropriate percentages math SAT 2500 Math 100 no Math 100 math SAT <500 Math 100 no Math 100 Grad. in 5 yrs 222 84 Doesn't Grad. in 5 vrs Graduate in 5 yrs 5 21 (c) Explain the seeming paradox, in language that the administrators can understand!

Answer 1

c) Comparing the percentage of graduates in 5 years between the two tables, we know that the difference of percentage of graduates in 5 years who score the math SAT scores more than 500 and less than 500 is comparatively smaller than the difference of percentage of graduates in 5 years who completes math 100 and doesn't complete math 100.