Question

Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks such as problemsolving. to demostrate this phenomenon, a sample of n=25 college students was given a problem solving task at noon on one day and againat 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 MD=4.7 points 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 with a=.05.
b. Compare an estimated Cohen's d to measure the size of the effect.

Answer 1

To evaluate the impact of sleep deprivation on problem-solving ability, a hypothesis test is conducted using a sample of college students' scores before and after a period of no sleep. The test compares the average difference in scores with the critical value from the t-distribution to determine significance. Furthermore, Cohen's d is calculated to measure the size of the effect.

Step-by-step explanation:

Given the sample size n=25, the average difference in scores MD=4.7, and the variance s2=64, we can conduct a hypothesis test to ascertain the significance of the change in problem-solving ability due to sleep deprivation. First, we calculate the standard deviation s by taking the square root of the variance, which gives us 8. Then, we use the formula for the t-statistic, which is t = MD / (s / sqrt(n)), resulting in a t-value. Comparing this value against the critical t-value from the t-distribution table for a two-tailed test with 24 degrees of freedom (n-1) at α=.05 helps us determine whether the change is significant.

To measure the effect size, we calculate Cohen's d using the formula d = MD / s, which provides insight into the practical significance of the difference in scores. A larger Cohen's d indicates a more substantial effect of sleep loss on problem-solving abilities.