SOLUTION: 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 show

Question 439673: 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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To test the hypothesis that students who finish an exam first get better grades. Professor kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with the 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 a= .05?
(a) State the hypothesis for a right -tailed test.
Ho: u(early)-u(later)=0
Ha: u(early)-u(later)> 0
--------------------
(b) Obtain a test statistic and p-value assuming equal variances. Interprest these results.
Run a 2-Sample T-Test to get:
test statistic: t = 1.2212
p-value = 0.1141...
Since p-value is greater than 5%, Fail to Reject Ho.
The professor is wrong.
---------------------------
(c) Is the difference in mean scores large enough to be important
The test says "no".
----------------------------->
(d) Is it reasonable to assume equal variances?
Ho: (s(early))^2 = (s(later))^2
Ha: they are not equal
-------------------------
F-score critical values :0.44 and 2.27
------------------------
Test statistic: F = 19.6^2/24.9^2 = 0.6196...
------------------------
Conclusion: Since test stat is not in either rejection interval, Fail to
reject Ho.
Statistically speaking, the variances are not different.
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Cheers,
Stan H.

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