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

SECTION 17.3 | The Chi-Square Test for Independence 573
consist of numerical scores (from an interval or ratio scale), it is appropriate to compute a
sample mean and use a t test to evaluate a hypothesis about the population mean. For example,
a researcher could measure the IQ for each individual in a sample of registered voters.
A t test could then be used to evaluate a hypothesis about the mean IQ for the entire population
of registered voters. On the other hand, if the individuals in the sample are classified
into nonnumerical categories (on a nominal or ordinal scale), you would use a chi-square
test to evaluate a hypothesis about the population proportions. For example, a researcher
could classify people according to gender by simply counting the number of males and
females in a sample of registered voters. A chi-square test would then be appropriate to
evaluate a hypothesis about the population proportions.
LEARNING CHECK
ANSWERS
1. A researcher uses a sample of 50 people to test whether they see any differences
in picture quality for plasma, LED, and LCD televisions. If the data produce
χ 2 = 5.75, then what decision should the researcher make?
a. Reject H 0
for α = .05 but not for α = .01.
b. Reject H 0
for α = .01 but not for α = .05.
c. Reject H 0
for either α = .05 or α = .01.
d. Fail to reject H 0
for α = .05 and α = .01.
2. The chi-square distribution is ______.
a. symmetrical with a mean of zero
b. positively skewed with all values greater than or equal to zero
c. negatively skewed with all values greater than or equal to zero
d. symmetrical with a mean equal to n − 1
3. In a chi-square test for goodness of fit _____.
a. Σf e
= n
b. Σf e
= Σf o
c. both Σf e
= n and Σf e
= Σf o
d. neither Σf e
= n nor Σf e
= Σf o
1. D, 2. B, 3. C
17.3 The Chi-Square Test for Independence
LEARNING OBJECTIVES
6. Define the degrees of freedom for the chi-square test for independence and locate
the critical value for a specific alpha level in the chi-square distribution.
7. Describe the hypotheses for a chi-square test for independence and explain how the
expected frequencies are obtained.
8. Conduct a chi-square test for independence.
The chi-square statistic may also be used to test whether there is a relationship between
two variables. In this situation, each individual in the sample is measured or classified on
two separate variables. For example, a group of students could be classified in terms of