Question 392762
 A researcher predicts that listening to music while solving math problems will
make a particular brain area more active. (that is the claim)
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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. (that is the sample mean)
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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. 
(that is the population data)
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(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.
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Ho: u = 35
Ha: u > 35 (claim)
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z(58) = (58-35)/10 = 23/10 = 2.3
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The critical region for a right tail test with alpha = 1% is z>2.3263
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Conclusion: Since the test statistic is less than z = 2.3263, reject Ho.
The test results support the claim.
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Cautionary Note.  Since the test statistic is barely in the reject interval
more testing is required.
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Cheers,
Stan H.
(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).