Question 175838: 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 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.
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. Interpret these results.
Using pooled data I get t = 1.2152 as test statistic.
The p-value is 0.1154 meaning at least 11.54% of test results could have
resulted in stronger evidence for rejecting Ho.
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(c) Is the difference in mean scores large enough to be important?
No, the p-value is too high to reject Ho.
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(d) Is it reasonable to assume equal variances?
Yes; this test does not give strong contrary evidence.
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(e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
I'll leave that to you.
Cheers,
Stan H.
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