Question 132260: Your help will be appreciated, I do not have an ISBN number because it's an online course:
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 diviation 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 alpha=.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 alpha=.05. show all steps cleary.
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 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 diviation 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 alpha=.05?
(a) state the hypotheses for a right tailed test.
Ho: mu(early)-mu(later) <= 0
Ha: mu(early)-mu(later) > 0 (this is the claim)
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(b) obtain a test statistic and p-value assuming equal variances.interpret these results.
I ran a "2-Sample T-test on a TI-83 calculator to get the following:
Test statistic: t=1.221156....
p-value = 0.22811...
df = 47
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Conclusion: Since p-value is greater than alpha=5%, Fail to reject Ho.
The instructors claim is not supported by the test results.
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(c) is the difference in mean scores large enough to be important?
Ans: No
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(d) is it reasonable to assume equal variances?
Ans: Need to look at answer on "e", below.
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(e) carry out a formal test for equal variances at alpha=.05. show all steps cleary.
Ho: variance(early)-variance(later) = 0
Ha: they are not equal
Critical F-values: 0.58, 2.00
Test statistic: F = 19.6^2/24.9^2 = 0.6196
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Conclusion: Since 0.58 < 0,6196 < 2.00, Fail to reject Ho.
The variances are statistically equal.
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Cheers,
Stan H.
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