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Chapter 15: Chi-Square Tests
The distribution depends on the degrees of freedom,
=
- 1, where
is the sample size.
The value of a
random variable is always nonnegative.
There are infinitely many
distributions, since each is uniquely defined
by its degrees of freedom.
For small sample size, the
distribution is much skewed to the right.
As
increases, the
distribution becomes more and more symmetrical.
Figure 15-1
displays some of the properties for the
distribution.
Since we will be using the
distribution for the hypothesis tests in this
chapter, we will need to be able to find critical values associated with the
distribution.
Note:
Values for the random variable with the appropriate degrees of freedom can
be obtained from the Critical Value for the Chi Square Distribution
workbook.
In order for us to perform hypothesis tests in this chapter, we need to be
familiar with the notation
(read as “chi-square sub alpha with
-
1
degrees of freedom”). Following is the definition for the notation
.
Definition:
is a
value with
-1 degrees of freedom such that
area is to the
right of the corresponding
value.
The diagram in
Figure 15-2
shows a pictorial representation that explains
the notation for
.