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 scanne

Question 392762: 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).
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. (that is the claim)
-------------------------
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)
-------------------------
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)
---------------------------
(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.
----
Ho: u = 35
Ha: u > 35 (claim)
---
z(58) = (58-35)/10 = 23/10 = 2.3
---
The critical region for a right tail test with alpha = 1% is z>2.3263
----
Conclusion: Since the test statistic is less than z = 2.3263, reject Ho.
The test results support the claim.
----
Cautionary Note. Since the test statistic is barely in the reject interval
more testing is required.
================================
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).

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