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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Researchers hate 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 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 μ = 45 and form a normal distribution with σ = 9.

a. Can the researcher conclude that the supplement has a significant effect on cognitive skill ? Use a two-tailed test with α = .05.

b. Compute Cohen's d for this study.

c. Write a .sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

a.

To determine
Whether the supplement has a significant effect on cognitive skills using a 2 tailed test with α=0.05.

Explanation

Given info:

The value of μ=45, M=50.2, σ=9, n=16 and α=0.05.

Calculation:

The null hypothesis H0, states that there the supplement had no significant effect on cognitive skills.

Null hypothesis:

H0:μ=45

Alternative hypothesis:

The alternative hypothesis H1, states that the supplement had significant effect.

H1:μ45

With α=0.05, the critical region comes with critical boundaries as z=±1

b.

To determine
Compute Cohen’s d to measure effect size.

c.

To determine

To write: A sentence demonstrating how the outcome of the hypothesis test and measure of effect size would appear in a research report.

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