3. A researcher predicts that listening to music
while solving math problems will make a particular brain area more active. To
test this, a research participant has her brain scanned while listening to
music and solving math problems, and the brain area of interest has a
percentage signal change of 58. From many previous studies with this same math
problem’s procedure (but not listening to music), it is known that the signal
change in this brain is normally distributed with a mean of 35 and a standard
deviation of 10.
the .01 level, what should the researcher conclude? Solve this problem
explicity using all five steps of hypothesis testing, and illustrate your
answer with a sketch showing the comparison distribution, the cutoff (or
cutoffs), and the score of the sample on this distribution.
Explain your answer to someone who has never had a
course in statistics (but who is familiar with mean, standard deviation, and Z scores).