Question 136511: Please help, no text book.
Consider this problem:
Instructor Dorff wants to test the hypothesis that students who finish an exam earlier .... get a better score.
She kept track of the order of the submission of a recent test;
>> the first 25 papers showed a mean score of 77.1 with std deviation of 19.6
>> the second 24 papers showed a mean score of 69.3 with std deviation of 24.9
>> state the hypothesis for a right tailed test and test at the 0.05 level of significance .. and determine if the difference in scores is significant
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2. To test the hypothesis that students who finish an exam first get better grades. Professor Dorff 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
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(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.
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(c) Is the difference in mean scores large enough to be important
The test says "no".
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(d) Is it reasonable to assume equal variances?
Ho: (s(early))^2 = (s(later))^2
Ha: they are not equal
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F-score critical values :0.44 and 2.27
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Test statistic: F = 19.6^2/24.9^2 = 0.6196...
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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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