Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidant in foods such as blueberries can reduce and even reverse those age-related declines, at least in laboratory rats (Joseph,et al.,1999). Based on these results, one might theorize that the same antioxidants might benefit elderly humans.  Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives and gives each participant a daily dose of 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 μ =45 and form a normal distribution with a σ = 9. Can the researchers conclude that the supplement significantly increases cognitive skills?   Use a one-tail (not two-tail)  test with α= .05.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidant in foods such as blueberries can reduce and even reverse those age-related declines, at least in laboratory rats (Joseph,et al.,1999). Based on these results, one might theorize that the same antioxidants might benefit elderly humans.  Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives and gives each participant a daily dose of 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 μ =45 and form a normal distribution with a σ = 9.

Can the researchers conclude that the supplement significantly increases cognitive skills?   Use a one-tail (not two-tail)  test with α= .05.

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