To test hypothesis that students who finish the exam first get better grades, Professor Hardtack kept track of order in which papers were managed in. The first 25 papers showed the mean score of 77.1 with 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 this a significant difference at α = .05?
(a) State hypotheses for right-tailed test.
(b) Obtain test statistic and p-value supposing equal variances. Interpret these results.
(c) Is the difference in mean scores large enough to be significant?
(d) Is it reasonable to suppose equal variances?
(e) Perform a formal test for equal variances at α = .05, showing all steps clearly.