Question 211120: 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 percent signal change of 58. From many previous
studies with this same math-problems procedure (but not listening to music), it
is known that the signal change in this brain area is normally distributed with a
mean of 35 and a standard deviation of 10. Using the .01 level, what should the
researcher conclude? Solve this problem explicitly 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. Then explain your answer to someone who has never had a course
in statistics (but who is familiar with mean, standard deviation, and Z score
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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 percent signal change of 58.
From many previous studies with this same math-problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10.
Using the .01 level, what should the researcher conclude?
--------------------------
Ho: u = 35
Ha: u > 35
-----------------
Critical Value: z = 2.326
Test statistic: z = (35-58)/10 = 2.3
p-value = P(z>2.3) = 0.0107
---------------------------------
Since the p-value is greater than 1%, do not reject Ho
But the decision is very close. More testing should be done.
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Cheers,
Stan H.
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