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

1. 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?