Question 128714: Please help me. I am having problem with this question. Taken from the Applied Stat and Economics.
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?
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(a) State the hypotheses for a right-tailed test.
Ho: mu(first) - mu(last) = 0
Ha: mu(first) - mu(last) > 0
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(b) Obtain a test statistic and p-value assuming equal variances.
Comment: Since the standard deviations are given and are different,
I did not assume equal variances in my calculations.
t(77.1-69.3) = 7.8/sqrt[19.6^2/25)+(24.9^2/24] = 1.2152
p-value = 0.1151
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Interpret these results.
Since the p-value is greater than 5%, fail to reject Ho.
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(c) Is the difference in mean scores large enough to be important?
No; the test show there is no significant statistical evidence
that the early papers are better than the later papers.
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(d) Is it reasonable to assume equal variances?
I don't know why you would.
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(e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
See part (b)
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Comment:
I don't know how the calculations are different if you assume equal
variances.
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Cheers,
Stan H.
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