1. Many students at Matt's school claim they can think more clearly while listening to their favorite kind of

music. Matt thinks music interferes with thinking clearly. To test this, he recruits 84 volunteers and

randomly assigns them to two groups. The "Music" group listens to their favorite music while playing a

"matching" memory game. The "No Music" group plays the same game in silence. Below are summary

statistics for the number of turns it took each subject to complete the game (fewer turns indicates a better

performance).

nmeansMusic4215.8333.944No music4213.7143.550

(a) Is there convincing evidence that listening to music increases the average number of turns required to

finish the memory game?

(b) Suppose Matt allowed people to choose whether or not they were in the group that listened to music

while playing the game. Explain how this might lead to confounding.

2. Aspirin, a longtime antidote for the side effects of drinking alcohol, may actually enhance alcohol's effect.

In a report published in the Journal of the American Medical Association, researchers found that aspirin

lowered the body's ability to break down alcohol in the stomach. Volunteers were used to test the effect of

aspirin on alcohol. Each of the 35 volunteers came to the research center twice. Once they ate a standard

breakfast and drank 2 glasses of wine. Another time they ate a standard breakfast, drank 2 glasses of wine

and took 2 extra-strength aspirin tablets. The mean difference (with aspirin - without aspirin) in their blood

alcohol levels was 0.02 with a standard deviation of 0.04. The researchers want to determine if aspirin

causes an increase in the mean difference in blood alcohol levels for volunteers like these.

(a) What additional information would you need to confirm that the conditions for this test have been met?

(b) Assume the conditions have been met. Calculate the standardized test statistic and P-value for this test.

(c) Interpret the P-value and draw the appropriate conclusion at the = 0.05 significance level.

(d) Given your conclusion in part (c), which type of error, Type I or Type II, could you have made?

Describe that error in the context of this study.