The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At= 0.01 level, is the student academic group's claim correct?

((Please try to do it in many steps so I can figure out how questions like these should be solved).