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

SECTION 17.2 | An Example of the Chi-Square Test for Goodness of Fit 569
FIGURE 17.2
Chi-square distributions
are positively skewed. The
critical region is placed
in the extreme tail, which
reflects large chi-square values.
0
x 2
Critical
region
The following example is an opportunity to test your understanding of the expected
frequencies and the df value for the chi-square test for goodness of fit.
EXAMPLE 17.1
A researcher has developed three different designs for a computer keyboard. A sample of
n = 60 participants is obtained, and each individual tests all three keyboards and identifies
his or her favorite. The frequency distribution of preferences is as follows:
Design A Design B Design C
23 12 25 n = 60
Assume that the null hypothesis states that there are no preferences among the three
designs. Find the expected frequencies for the chi-square test and determine the df
value for the chi-square statistic. You should find that f e
= 20 for all three keyboard
designs and df = 2.
■
df 5 1
df 5 5
df 5 9
FIGURE 17.3
The shape of the chi-square
distribution for different
values of df. As the number
of categories increases,
the peak (mode) of the
distribution has a larger
chi-square value.
0
x 2