To test the hypothesis that students finish an exam first getbetter grades, Prof

Question

To test the hypothesis that students finish an exam first getbetter grades, Professor hardtrack kept track of the order in whichpapers were handded in. The first 25 papers showed a mean score of77.1 with a standard deviation of 19.6, while the last 24 papershanded in showed a mean score of 69.3 with a standard deviation of24.9. Is this a significant differeence at a= .05? a) State the hypothesis for a right tailed test b) Obtain a test statistic and p value assuming equalvariances. Interpret these results. c) Is the difference in mean scores large enough to beimportant? d) Is it reasonable to assume equal variances? e)Cary out a formal test for equal variances at a =.05,showing all steps clearly. To test the hypothesis that students finish an exam first getbetter grades, Professor hardtrack kept track of the order in whichpapers were handded in. The first 25 papers showed a mean score of77.1 with a standard deviation of 19.6, while the last 24 papershanded in showed a mean score of 69.3 with a standard deviation of24.9. Is this a significant differeence at a= .05? a) State the hypothesis for a right tailed test b) Obtain a test statistic and p value assuming equalvariances. Interpret these results. c) Is the difference in mean scores large enough to beimportant? d) Is it reasonable to assume equal variances? e)Cary out a formal test for equal variances at a =.05,showing all steps clearly.

Explanation / Answer

          a.        H0: m1 =m2 versus H1:m1 > m2.

           b.     t = 1.221, p-value =.1141

           c.     The results of the sample are notstatistically significant although students might think 8 points isan important difference.

           d.     Yes, the sample standard deviationsappear similar.

           e.     F = .620.FL = 0.488, FR = 2.05. Failto reject the null hypothesis. This sample does not provideevidence that the variances are different.

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