Scientists wanted to test whether regular exercise can help increase sleep duration They randomized 180 sedentary male volunteers who don't regularly exercise between a treatment group and a
control group. The treatment group was instructed to perform aerobic exercise for about an hour per day over a
period of 10 weeks, and the control group was instructed to continue with their exercise-less routine. The sleep
duration of each subject was measured (in minutes) just before and right after the treatment period.
The results of the experiment showed that the mean change in sleep duration of the treatment group is 50
minutes greater than the mean change of the control group. To test whether the results could be explained by
random chance, the researchers created the table below, which summarizes the results of 1000 re-
randomizations of the data (with differences between means rounded to the nearest 10 minutes).
According to the simulations, what is the probability of the treatment group's mean being higher than the
control group's mean by 50 minutes or more?
Assume that if the probability you found is lower than 5%, then the result should be considered significant