Posted by Anonymous on Friday, January 13, 2012 at 11:47pm.
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 mathproblems 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).

Ho: u = 35
H1: u > 35

test stat: z(58) = (5835)/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.
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Cheers,
Stan H.

statistics  PsyDAG, Saturday, January 14, 2012 at 12:05pm
Good job.