# Testing the Different Performance of Students with and without Sleep

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a. Research has shown that losing a few hours of sleep can have a significant effect on performance of some simple tasks. To demonstrate this phenomenon, a sample of n = 25 college students was given a simple problem solving task at noon one day and again at noon on the following day. The students were not permitted any sleep a full night between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged Md = 4.7 better on the first test with a variance of 64 for the difference of scores.

b. Do the data indicate a significant change in problem solving ability? Use a two tailed test with ?=.01. Be sure to show all formulas, steps, processes and calculations for all parts of the

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This solution shows how to calculate the test statistic and the critical value and interpret the results. The expert determines if the data indicates a significant change in problem solving abilities.

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Hypothesis: Ho: mud is 0 vs. Ha: mud is not 0 where mud is the true mean differnce of the first and second ...

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