Chapter 11, Problem 10P

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 s² = 64 for the difference scores.

a. Do the data indicate a significant change in problem-solving ability? Use a two-tailed test with $\alpha$ = .05.

b. Compute an estimated Cohen's d to measure the size of the effect.