Question: Two professors teach different sections of the same course. One professor, Dr. Easy, has a reputation for being an easy grader. The other professor, Dr.
Two professors teach different sections of the same course. One professor, Dr. Easy, has a reputation for being an easy grader. The other professor, Dr. Hard, has a reputation for being a demanding grader.
While it is true that these two professors' grades do tend to differ in the direction of their reputations, the division dean suspects that the reason for the difference may be that Dr Easy's class typically includes more underclass (UNC) students, and underclass students are simply less well prepared for the course.
To test her hypothesis, the division dean matches students between the two sections on class year. She leaves out students who don't have a match in the other section. Then, she compares the students' final courses grades.
Here are the results:
Dr. Easy
87
75
82
94
77
76
68
90
76
69
86
93
94
83
90
86
Pair
1 (UPC)
2 (UNC)
3 (UNC)
4 (UPC)
5 (UPC)
6 (UNC)
7 (UNC)
8 (UPC)
9 (UPC)
10 (UNC)
11 (UNC)
12 (UPC)
13 (UNC)
14 (UPC)
15 (UPC)
16 (UNC)
Dr. Hard
85
70
86
84
83
75
71
90
84
67
80
89
90
89
94
85
- Please state the null and alternative hypotheses in this scenario.
b. Please compute the independent-samples t-test. Please state its associated p-value. What decision would you make about which hypothesis to believe at a Type I alpha error rate (p-value) of 0.05?
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