x2 Test Finding p-values for Contingency Tables

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:

Ho: The Matrix entries represent Independent events.
Ha: The Matrix entries represent events that are not independent.

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


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.