(Solution) - Two professors teach different sections of the same course One -(2025 Original AI-Free Solution)

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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 hard grader. While it is true that the 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 upper-class (UPC) students, while Dr. Hard'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 students' final course grades. Here are the data:

a. State the division dean's research hypothesis. Note that this is one of those infer - quent times when the research hypothesis will be supported by finding no difference rather than by finding a significant difference.
b. Calculate t and compare it with the one-tailed critical t at the .05 a level. Did Dr. Hard's students earn significantly lower grades than Dr. Easy's students?