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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 scores).
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Ho: u = 35
H1: u > 35
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test stat: z(58) = (58-35)/10 = 23/10 = 2.3
58 is 2.3 standard deviations above the hypothesized mean of 35
---------------
Test results this far or further above the mean have slightly more
than 1% chance of occuring.
You could claim, with nearly 99% assurance, that the music helped.
====================
Cheers,
Stan H.

  • statistics -

    Good job.

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