1. There was a rumor circulating that one instructor's exams are more difficult than was another instructor. Some students were concerned that the average time for Instructor B was more than 12 minutes longer than for Instructor A. A sample of 32 times to complete a test was obtained from Instructor A and a sample of 32 times to complete a test was obtained from instructor B. The results were as follows Instructor A Instructor B Difference Sample size 32 32 32 Sample average 127.4 141.3 -13.9 Sample Variance 31.92 46.11 42.96 Is there sufficient evidence at the 201 level of significance to confirm the students concern? What is the P-value of your test statistic? 2. A statistics instructor believes that if the statistics requirement were a two quarter sequence the students who were having more difficulty would benefit from the extra time. The instructor conducts a survey among former students. The instructor chooses at random 80 former students who had done well and asks if they would have preferred a two quarter course. A random sample of 80 former students who had not done well is also asked if they would have preferred a two quarter course. The results of the survey appear below: Done well Not Done Well Difference Sample size 80 80 80 Prefer two quarters 8 20 -12 Not prefer two quarters 72 60 12 Is there sufficient evidence at the 210 level of significance to indicate that the students who did not do well had a higher preference for a two quarter sequence? What is the P-value of your test statistic