A professor wants to see how much students learn over the course of a semester. A pre-test is given before the class begins to see what students know ahead of time, and the same test is given at the end of the semester to see what students know at the end. The data are below. Test for an improvement at the = 0.05 level. Did scores increase? How much did scores increase?
Pretest (X1) Posttest (X2) D
90 89
60 66
95 99
93 91
95 100
67 64
89 91
90 95
94 95
83 89
75 82
87 92
82 83
82 85
88 93
66 69
90 90
93 100
86 95
91 96