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

APPENDIX C | Solutions for Odd-Numbered Problems in the Text 681
17. The null hypothesis states that there is no difference
between the distribution of preferences predicted by
women and the actual distribution for men. With
df = 3 and α = .05, the critical value is 7.81. The
expected frequencies are:
Somewhat
thin
Slightly
thin
Slightly
heavy
Somewhat
heavy
Women 22.9 22.9 22.9 11.4
Men 17.1 17.1 17.1 8.6
Chi-square = 9.13. Reject H 0
and conclude that there
is a significant difference in the preferences predicted
by women and the actual preferences expressed by
men.
19. a. The null hypothesis states that there is no
relationship between IQ and volunteering. With
df = 2 and α = .05, the critical value is 5.99.
The expected frequencies are:
IQ
High Medium Low
Volunteer 37.5 75 37.5
Not volunteer 12.5 25 12.5
The chi-square statistic is 4.75. Fail to reject H 0
with
α = .05 and df = 2.
21. The null hypothesis states that there is no relationship
between the season of birth and schizophrenia. With
df = 3 and α = .05, the critical value is 7.81. The
expected frequencies
Summer Fall Winter Spring
No Disorder 23.33 23.33 26.67 26.67
Schizophrenia 11.67 11.67 13.33 13.33
Chi-square = 3.62. Fail to reject H 0
and conclude that
these data do not provide enough evidence to conclude
that there is a significant relationship between
the season of birth and schizophrenia.
23. a. The null hypothesis states that there is no relationship
between gender and willingness to use mental
health serviced. With df = 2, the critical value is
5.99. The expected frequencies are:
Willingness to Use Mental
Health Services
Probably No Maybe Probably Yes
Males 12 30 18 60
Females 18 45 27 90
30 75 45
Chi-square = 8.23. Reject the null hypothesis.
b. Cramér’s V = 0.234.
CHAPTER 18
The Binomial Test
1. H 0
: p(accident involves a driver aged 20 or younger)
= 0.15 (15%): The distribution of ages for accidents
is not different from the distribution of ages for
licensed drivers. The critical boundaries are
z = ±1.96. With X = 26, μ = 12, and σ = 3.19,
we obtain z = 4.39. Reject H 0
and conclude that
there is a significant difference.
3. a. H 0
: p = q = 1 2 (no advantage for one color over
the other). The critical boundaries are z = ±1.96.
With X = 31, μ = 25, and σ = 3.54, we obtain
z = 1.69. Because the z-score is not in the critical
region, the data do not show a significant
difference in winning percentage between the
two colors.
b. With X = 62, μ = 50, and σ = 5, we obtain
z = 2.40. Because the z-score is in the critical
region, the data show a significant difference in
winning percentage between the two colors.
c. With a small sample (part a) a winning percentage
of 62% is not significantly different from 50%,
but with a larger sample (part b) the difference is
enough to be significant.
5. H 0
: p = q = 1 2 (no preference). The critical boundaries
are z = ±1.96. With X = 28, μ = 20, and σ = 3.16,
we obtain z = 2.53. Reject H 0
. There is evidence of a
significant preference between bottled water and tap
water.
7. H 0
: p = q = 1 2 (no preference). The critical boundaries
are z = ±2.58. With X = 92, μ = 75, and σ = 6.12,
we obtain z = 2.77. Reject H 0
, there is a significant
preference for technical skill.
9. a. H 0
: p(accident) = 0.12 (no change). The critical
boundaries are z = ±1.96. With X = 45,
μ = 60, and σ = 7.27, we obtain z = −2.06.
Reject H 0
, there has been a significant change
in the accident rate.