Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

PROBLEMS 525
9. With a small sample, a single point can have a large
effect on the magnitude of the correlation. To create the
following data, we started with the scores from problem
8 and changed the first X value from X = 3 to X = 8.
X
Y
8 6
5 5
6 0
6 2
5 2
a. Sketch a scatter plot and estimate the value of the
Pearson correlation.
b. Compute the Pearson correlation.
10. For the following set of scores,
X
Y
4 5
6 5
3 2
9 4
6 5
2 3
a. Compute the Pearson correlation.
b. Add two points to each X value and compute the
correlation for the modified scores. How does adding
a constant to every score affect the value of the
correlation?
c. Multiply each of the original X values by 2 and
compute the correlation for the modified scores.
How does multiplying each score by a constant
affect the value of the correlation?
11. Correlation studies are often used to help determine
whether certain characteristics are controlled more
by genetic influences or by environmental influences.
These studies often examine adopted children and compare
their behaviors with the behaviors of their birth
parents and their adoptive parents. One study examined
how much time individuals spend watching TV (Plomin,
Corley, DeFries, & Fulker, 1990). The following
data are similar to the results obtained in the study.
Amount of Time Spent Watching TV
Adopted Children Birth Parents Adoptive Parents
2 0 1
3 3 4
6 4 2
1 1 0
3 1 0
0 2 3
5 3 2
2 1 3
5 3 3
a. Compute the correlation between the children and
their birth parents.
b. Compute the correlation between the children and
their adoptive parents.
c. Based on the two correlations, does TV watching
appear to be inherited from the birth parents or is it
learned from the adoptive parents?
12. In the Chapter Preview we discussed a study by Judge
and Cable (2010) demonstrating a negative relationship
between weight and income for a group of
women professionals. The following are data similar
to those obtained in the study. To simplify the weight
variable, the women are classified into five categories
that measure actual weight relative to height, from
1 = thinnest to 5 = heaviest. Income figures are annual
income (in thousands), rounded to the nearest $1,000.
a. Calculate the Pearson correlation for these data.
b. Is the correlation statistically significant? Use a
two-tailed test with α = .05.
Weight (X)
Income (Y)
1 115
1 78
4 53
3 63
5 37
2 84
5 41
3 51
1 94
5 44
13. The researchers cited in the previous problem also
examined the weight/salary relationship for men and
found a positive relationship, suggesting that we have
very different standards for men than for women
(Judge & Cable, 2010). The following are data similar
to those obtained for a sample of male professionals.
Again, weight relative to height is coded in five
categories from 1 = thinnest to 5 = heaviest. Income
is recorded as thousands earned annually.
a. Calculate the Pearson correlation for these data.
b. Is the correlation statistically significant? Use a
two-tailed test with α = .05.
Weight (X)
Income (Y)
4 151
5 88
3 52
2 73
1 49
3 92
1 56
5 143