An assistant professor designs his fall semester class so that a major homework assignment is due the day his students waltz into class to take their first exam

The results are mixed so he rewrites his exam for the spring semester and repeats the process, again collecting a major homework assignment on exam day and grading and returning both the homework assignments and exams the following class meeting. Use an appropriate tool from the tools for continuous improvement to analyze the data. What conclusions do you draw?

Homework grade Exam Grade Spring Exam Grade Fall
2 18 51
5 20 34
13 20 36
14 23 69
16 23 46
16 24 60
19 29 20
20 29 66
22 29 44
28 30 53
29 31 42
30 32 40
31 35 55
33 42 65
36 45 54
38 48 59
57 48 26
59 50 49
67 54 32
67 62 43
72 62 60
82 66 34
98 67 55

What will be an ideal response?

Answer: The best tool for this occasion would be the scatter diagram. Plotting exam score against homework grade yields some insight.

Since the homework is completed and due before the exam experience, it is reasonable to test whether performance on the exam depends on performance on the homework. This does not appear to be the case in the fall semester; as homework grade improves from near zero to near 100, the level of exam score doesn't change significantly. The spring semester data tell a different story. There is a marked change in level as homework grade improves, suggesting that diligence on homework in some way prepares the student for an exam. Truly a remarkable notion.