To test the hypothesis that students who finish an exam first get better grades, Prof. Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is there sufficient evidence to support Prof. Hardtack's hypothesis, at α = 0.05? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at α = 0.05, showing all steps clearly.