Hypothesis testing for difference between two means.
To test the hypothesis that students who finish an exam first get better grades, Professor 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, as the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this an important difference at _ = .05?
(a) Status 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 suppose equal variances?
(e) Carry out a formal test for equal variances at _ = .05, showing all steps clearly.