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

PROBLEMS 597
Finally, we can add the last column to get the chi-square value.
χ 2 = 5.71 + 4.57 + 1.14 + 13.33 + 10.67 + 2.67
= 38.09
STEP 4
Make a decision about H 0
, and state the conclusion The chi-square value is in the critical
region. Therefore, we can reject the null hypothesis. There is a relationship between watch
preference and age, χ 2 (2, n = 200) = 38.09, p < .05.
DEMONSTRATION 17.2
PROBLEMS
EFFECT SIZE WITH CRAMÉR’S V
Because the data matrix is larger than 2 × 2, we will compute Cramér’s V to measure
effect size.
Cramér’s V = Î x2
nsdf*d
Î 5 38.09 5 Ï0.19 5 0.436
200s1d
1. Parametric tests (such as t or ANOVA) differ from
nonparametric tests (such as chi-square) primarily in
terms of the assumptions they require and the data
they use. Explain these differences.
2. The student population at the state college consists of
60% females and 40% males.
a. The college theater department recently staged
a production of a modern musical. A researcher
recorded the gender of each student entering
the theater and found a total of 37 females and
18 males. Is the gender distribution for theater
goers significantly different from the distribution
for the general college? Test at the .05 level of
significance.
b. The same researcher also recorded the gender of
each student watching a men’s basketball game in
the college gym and found a total of 58 females
and 82 males. Is the gender distribution for
basketball fans significantly different from the
distribution for the general college? Test at
the .05 level of significance.
3. A developmental psychologist would like to determine
whether infants display any color preferences. A
stimulus consisting of four color patches (red, green,
blue, and yellow) is projected onto the ceiling above a
crib. Infants are placed in the crib, one at a time, and
the psychologist records how much time each infant
spends looking at each of the four colors. The color
that receives the most attention during a 100-second
test period is identified as the preferred color for that
infant. The preferred colors for a sample of 80 infants
are shown in the following table:
Red Green Blue Yellow
25 18 23 14
a. Do the data indicate any significant preferences
among the four colors? Test at the .05 level of
significance.
b. Write a sentence demonstrating how the outcome
of the hypothesis test would appear in a research
report.
4. Data from the Motor Vehicle Department indicate that
80% of all licensed drivers are older than age 25.
a. In a sample of n = 50 people who recently
received speeding tickets, 33 were older than
25 years and the other 17 were age 25 or younger.
Is the age distribution for this sample significantly
different from the distribution for the population of
licensed drivers? Use α = .05.
b. In a sample of n = 50 people who recently
received parking tickets, 36 were older than
25 years and the other 14 were age 25 or younger.
Is the age distribution for this sample significantly
different from the distribution for the population of
licensed drivers? Use α = .05.
5. Research has demonstrated that people tend to
be attracted to others who are similar to themselves.
One study demonstrated that individuals are