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.
------------------------------
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
Ho: u = 0.35
Ha: u is not equal to 0.0.35
----------------------------------------
z(0.58) = (0.58-0.35)/0.10 = 2.3
p-value = 2P(z > 2.3) = 0.0214
-----------------------------------------
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.
--------------------------------------------------------
Illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.
---
This site does not support graphing normal distributions and marking those
illustrations.
---------------.
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).
---
I hope ou can handle this last.
----------------------------------
Cheers,
Stan H.
|
|
|
