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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, 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 á = .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 á = .05, showing
all steps clearly.

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