To test the hypothesis that students who finish the exam first get better grades, Professor Hardtack kept track of order in which papers were handed 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 mean score of 69.3 with standard deviation of 24.9. Is this significant difference at _ = .05?
a) Describe the hypotheses for a right-tailed test.
b) Obtain the test statistic and p-value assuming supposing equal variances. Interpret these results.
c) Is the difference in mean scores large enough to be significant?
d) Is it reasonable to assume equal variances?
e) Carry out a formal test for equal variances at _ = .05, showing all steps clearly.