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 α = .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 = .05, showing all steps clearly.
The solution provides step by step method for the calculation of test statistic for population mean. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.