SOLUTION: 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;

Question 136232: 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(48568) (Show Source):
You can put this solution on YOUR website!
To test the hypothesis that students who finish an exam first get better grades. Instructor 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. Interpret 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 instructor is wrong.
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Cheers,
Stan H.