Our goal in this section is to illustrate how the TI-84 calculator can be used to perform tests on categorical data. Although the TI-84 is used in secondary schools, this topic is not normally covered at the secondary level in Canada.

Example 1, genetic ratios (one-way table)…chi^{2}cdf(0, chi_{c}, df) = .95 or .99

A more general form of the chi-squared test is used to determine whether two or more population characteristics are related in some way. A student council, for example, may be interested in the proportion of students passed by three statistics professors. The council learns that the number of students passed and failed by Professors U., V., and W last term were **A** = [r1; 56 50 62: r2; 7 21 12],

where A is a ‘TI-83 plus’ matrix.

In particular, A is the observation matrix, which contains the counts of students passed by each professor in the first row and the corresponding failure counts in the second row. In order to test for association.. a council member executes the TI-83 plus command **Test** using matrix A as input. The result is = 8.0005… ~ 8.00. A sufficiently large value for this statistic suggests that the two characteristics are not independent, i.e. they are related. Since chi^{2}cdf(0, 5.99, 2) = .94966… ~ 0.95, the critical value for the chi-squared statistic is 5.99 at the .05 significance level. Now, 8.00 > 5.99, so we reject the null hypothesis at the .05 significance level. However, chi^{2}cdf(0, 9.20, 2) = .98994… ~ 0.99, so the critical value for the chi-squared statistic is 9.20 at the .01 significance level. Since 8.00 < 9.20, we cannot reject the null hypothesis at the .01 significance level. The overall conclusion, based on the council’s data is… computes a chi^{2} test for association on the two-way (contingency) table of counts in the specified observed matrix, A…before executing chi^{2}Test, enter the observed counts in a matrix, A.