52.docx - 5.4 Chi-Square Test of Goodness of Fit and...

5.4 Chi-Square Test of Goodness of Fit and Independence
The X
2
(chi-square) distribution is used to test (1) if observed frequencies differ
“significantly” from expected frequencies when more than two outcomes are
possible; (2) if the sample distribution is binomial, normal, or other; and (3) if two
variables are independent or not.
 
encies ectedfrequ
f
f f
e
e
exp f
s frequencie observed f
Where
(5.4)
e
0
2
0
2






If the calculated X 2 is greater than the tabular value of X 2 at the specified level of
significance and degrees of freedom (from App.6), the null hypothesis, H
0
, is
rejected in favor of the alternative hypothesis, H