Question 126177This question is from textbook Applied Statistics in Business and Economics
: Please provide assistance for the following problem/questions. Thanks!
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 the .05 level of significance? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interpret the 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 the .05 level of significance, showing all steps clearly.
This question is from textbook Applied Statistics in Business and Economics
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 the .05 level of significance?
(a) State the hypotheses for a right-tailed test.
Ho: mu1-mu2 = 0
Ha: mu1-mu2 > 0
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(b) Obtain a test statistic and p-value assuming equal variances. Interpret the results.
t(77-69.3) = (7.8-0)/sqrt[(19.6^2/25)+(24.9^2/24)] = 7.8/6.4187=1.2152
p-value =0.1121
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Conclusion: Since p-value is greater than 5%, fail to reject Ho.
The results of the early papers and the later one are no statistically
different.
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(c) Is the difference in mean scores large enough to be important?
No
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(d) Is it reasonable to assume equal variances?
Ho: s1^2 = s2^2
Ha: s1^2 is not equal to s2^2
Test Statistic:
F = 19.6^2/24.9^2 = 0.6196
Critical Value:
df for numerator = 24 ; df for denominator = 23
F = 1.9838
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Conclusion:
Since the test statistic is less than the critical value fail to
reject Ho; the variances of the two groups of papers are statistically
equivalent.
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(e) Carry out a formal test for equal variances at the .05 level of significance, showing all steps clearly.
Done above.
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Cheers,
Stan H.
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