Aprofessor believes the class he is teaching in the current semester is above the average of the classes he has taught. in order to test this hypothesis, he analyses the scores of midterm of all 120 students he teaches this semester. their average score of this exam is 82 out of 100, with a standard deviation of 12. the mean score of the midterm for all students that he has taught for the last thirty-two years is 78 out of 100, with a standard deviation of 15. use an alpha level of 0.01 for this analysis.