1. A community college math department uses the same final exam for all college algebra students.The department chair is concerned that students in online courses do not do well as students in on-site courses.She takes a random sample of 40 on-site students and 35 online students and determines the final exam score for each student.The mean score for the on-site students is 75 with a standard deviation of 12.The mean score for the online students is 72 with a standard deviation of 15. Conduct a test at the 5% level of significance to determine if the mean score for all on-site students is higher than the mean score for all online students.
2. The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272 with standard deviation 78. Do we have evidence to support the claim that young men nationwide have a mean score below 275 at significance level 5%?