This test is also called the "Test for Independence". The TI-83PLUS
has a built-in c2 function, found under the "distr" menu. Recall the
basis for the chi-squared test; two events are independent if 
.
As always the calculator
returns the p-value and we reject Ho if p < 
.
The Hypotheses are
Ho:
The matrix entries represents independent events.
Ha: The
matrix entries represent events which are not independent.
All we
need to do is enter the observed values as Matrix[A], and the expected
values as Matrix [B].
To calculate each entry for the expected Matrix, [B] simply multiply that row total and that column total then divide the product by the grand total.
Example: A study of 500 males by a graduate statistics student was conducted to determine whether religious affiliation had an effect on divorce rate. At the 99% level of confidence test to see whether there is sufficient evidence to conclude religious affiliation does have an effect on divorce rate. The collected data is as follows:
Our Observed Matrix will be [A] = 
Our Expected Matrix will be [B] =
The hypothesis for this problem is as follows:
First, access the Matrix Menu and enter all values for both Matrices.
Press MATRIX Arrow right to EDIT
1 : [A] 1x1 will be highlighted,
Press 
Enter the dimensions of
our Observed Matrix. (2 by 5) (see screen below right)
 |  |
Press (see screen above right)
Match these settings. Observed: [A] Expected: [B]. Arrow down to
Calculate
Press
As you can see from the screen the p-value = 0.129. Since the p-value is not less than a we do not reject Ho.
There is not statistical evidence at the a = 0.01 level to conclude the male divorce rate depends on religious affiliation.