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    Hypothesis Testing

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    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).

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