+165
Behavioral scientists want to test whether classical music has a relaxing effect on patients with extreme anxiety. They decide to consider sleepiness as an indication that the patient is relaxed.
They randomized 100 patients in a hospital between a treatment group and a control group, and they put the groups in separate rooms. The treatment group had classical music playing in its room whereas the control group had a day without music.
The results of the experiment showed that the mean portion of time the treatment group spent sleeping that day was 15 minutes greater than the mean portion of time the control group spent sleeping. To test whether the results could be explained by random chance, the scientists created the table below, which summarizes the results of the 1,000 rerandomized trials of the data (with differences of means rounded to the nearest 5 minutes).
Treatment Group Mean − Control Group Mean Frequency
−25 7
−20 25
−15 69
−10 130
−5 160
0 188
5 172
10 34
15 68
20 36
25 11
According to the simulations, what is the probability that the treatment group mean is greater than the control group mean by 15 minutes or more, and what can be concluded regarding this result? Assume a probability of less than 5% is significant.
A The probability that the treatment group mean is 15 minutes or greater than the control group mean is 11.5%, and the results suggest that the original difference of means could be the result of random chance.
B The probability that the treatment group mean is 15 minutes or greater than the control group mean is 11.5%, and the results suggest that classical music makes anxious people sleepier
C The probability that the treatment group mean is 15 minutes or greater than the control group mean is 4.7%, and the results suggest that classical music makes anxious people sleepier.
D The probability that the treatment group mean is 15 minutes or greater than the control group mean is 1.1%, and the results suggest that classical music makes anxious people sleepier.
