## 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

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.