Many students at Matt’s school claim they can think more clearly while listening to their favorite kind of music. Matt believes that music interferes with thinking clearly. To find out which is true, Matt recruits 84 volunteers and randomly assigns them to two groups. The “Music” group listens to their favorite music while playing a “match the animals” memory game. The “No Music” group plays the same game in silence. Here are some descriptive statistics for the number of turns it took the subjects in each group to complete the game (fewer turns indicate a better performance):

Matt wants to know if listening to music affects the average number of turns required to finish the memory game for students like these.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

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Group Sample size Mean SD 305 = 0.200 = 20.0%s1 305 Music 0.200 = 20.0%n, 305 = 0.200 = 20.0%F1 = 15.833 42 nl=421526 x 1=15.8331526 sl=3.9441526 305 305 = 0.200 = 20.0%72 305 13.714 $2=3.5501526 No 0.200 = 20.0%n, = 42 0.200 = 20.0% s2 = x 2=13.7141526 %3D music n2=421526