Research has shown that losing even one night\'s sleep can have a significant ef

Question

Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks, such as problem solving (Linde & Bergstroem, 1992) To demonstrate this phenomenon, a sample of n = 25 college students was given a problem solving task at noon on one day and again at noon on the following day The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged M_D = 4.7 points better on the first test with a variance of s^2 = 64 the difference scores. Do the data indicate a significant change in problem-solving ability? Use a two-tailed test with alpha = .05. Compute an estimated Cohen's d to measure the size of the effect. This assignment allows submissions using both the text box below and attached documents. Type your comments in the box below and use Add Attachments button to include other documents. Save frequently while working.

Explanation / Answer

We have to test the null hypothesis

H0: µd=0 versus the alternative H1: µd0

Paired observations were taken so we will apply paired sample t-test

Test statistic t= (Md-µd)/sqrt(s^2/n)= (4.7-0)/sqrt(64/25) =2.94

Degree of freedom =n-1=25-1=24

p-value=0.0072 using excel function =TDIST(2.94,24,2)

Asp-value <0.05, so at =0.05 level, we reject the null hypothesis and conclude that there is a significant change in problem-solving ability.

Cohen’s d=(Md-µd)/sqrt(s^2)= (4.7-0)/sqrt(64) =0.5875

As d>0.50 , so there is large effect of sleep on problem solving ability.

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