Question 1085940: Researchers have noted a decline in cognitive functioning as people age. However the results from other research suggest that the antioxidants in foods such a blueberries can reduce and even reverse these age related declines, at least in lab rats. Based on these results, one might theorize that the same antioxidants might also benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n= 16 audlts who are older than 65 and gives each participant a daily dose of a blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce a mean score of M= 50.2. For the general population of elderly adults, scores on the test average p=45 and form a normal distribution with o=9.
Can the researcher conclude that the supplement has a significant effect on cognitive skill? Use a two-tailed test with a=0.05.
The standard error is ______, and z=_______, which _______ beyond the critical boundary of _______. __________ the null hypothesis, and conclude that the supplement ______ significant effect on cognitive performance.
Compute Cohen's d for this study
The blueberry supplement _________ a significant effect on cognitive skill scores: z= ______, p<_____, d=_______
I tried solving for Cohen's d with the formula mean difference/ standard deviation and i got 0.578. im not sure if that is correct.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Know population sd so z-test
SE is sigma/sqrt(n)=9/sqrt(16)=9/4
z=(x-mean)/SE=5.2/2.25=2.31
this is beyond the critical boundary of |z|>1.96 so reject Ho and conclude that the supplement does affect cognitive performance.
Cohen's d requires difference in mean over a pooled sd. There is only 1 sd here, so if that is assumed to be the sd, the difference in means is 5.2/9=0.578 as you have.
z=+2.31
p=0.0208 (multiply the probability at 2.31 by 2, because this should be 2-tail (could affect cognition adversely, too).
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