SOLUTION: 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

Question 188113: 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 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).

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 percent signal change of 58.
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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.
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Using the .01 level, what should the researcher conclude?
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Solve this problem explicitly using all five steps of hypothesis testing
Ho: u = 0.35
Ha: u is not equal to 0.0.35
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z(0.58) = (0.58-0.35)/0.10 = 2.3
p-value = 2P(z > 2.3) = 0.0214
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Conclusion: since the p-value is greater than 1%, Fail to reject Ho.
The result of this one test is not sufficient evidence to reject
the belief that the mean percentage is 0.35.
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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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This site does not support graphing normal distributions and marking those
illustrations.
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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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I hope ou can handle this last.
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Cheers,
Stan H.

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