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Psy 315 Chapter#4 - 18

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18. 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 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.
(a) 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.
(b) Then explain your answer to someone who has never had a course in statistics (but who is
familiar with mean, standard deviation, and Z scores).
H0: μ = 35
H1: μ ≠ 35
α = 0.01
Critical Z values = ±2.5758
Z = (-μ)/ (σ) = (58-35)/ (10) = 2.3
Since 2.3 < 2.5758 we fail to reject H0 and therefore the researcher is unable to reject the
probability that the mean of signal change is 35. The difference is not significant at α = 0.01.
The z-score that was established here lies outside the critical region. Critical region is a set of
values of the test statistic or the z-score which rejects the possibility of the conclusion being
false.

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18. 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 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. (a) Using the .01 level, what should the researcher conclude? Solve th ...
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