Question 983600: 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 problem’s procedure (but not listening to music), it is known that the signal change in this brain 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.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho=there is no significant difference. mu=35
Ha=there is a significant difference. mu not equal to 35.
Two-tailed test
alpha=0.01
test statistic is z=(x-mu)/sd
critical value is at z.005 and z.995
if abs(z)>2.576, we will reject the null hypothesis
Calculation: z=(58-35)/10=+2.3
Fail to reject the null hypothesis. There is insufficient evidence to assume the brain percentage of signal change is different from the mean at the 0.01 level.
I would draw a normal curve, and put vertical lines at -2.576 and +2.576, shading everything to the left and right respectively. I would put the sample value at +2.3, showing that it is not within the cutoff region.
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