had to take 2 pictures.. 20. Chapter 8, Problem 18 Aa Aa Researchers have noted

Question

had to take 2 pictures..

20. Chapter 8, Problem 18 Aa Aa Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999). 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 adults who are d 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 = 45 and form a normal distribution with = 9. Can the researcher conclude that the supplement has a significant effect on cognitive skill? Use a two-tailed test with .05. Standard Normal Distribution Standard Deviation1.0

Explanation / Answer

Given that,
population mean(u)=45
standard deviation, =9
sample mean, x =50.2
number (n)=16
null, Ho: =45
alternate, H1: !=45
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 50.2-45/(9/sqrt(16)
zo = 2.31111
| zo | = 2.31111
critical value
the value of |z | at los 5% is 1.96
we got |zo| =2.31111 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 2.31111 ) = 0.02083
hence value of p0.05 > 0.02083, here we reject Ho
ANSWERS
---------------
null, Ho: =45
alternate, H1: !=45
test statistic: 2.31111
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.02083

Cohen's D = |X-U/| = |(50.2-45)/9| = 0.5777

the effective size is medium
the supplement has a significant effect on cognitive skill

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