Question

State the critical value of ?2 and determine the appropriate conclusion for a chi-square test for
association using the given information.
a) ? = 0.025, Number of rows = 5, Number of columns = 5, ?2 = 31.1
b) ? = 0.10, Number of rows = 7, Number of columns = 6, ?2 = 40.3

Answer 1

a) The number of degrees of freedom here is computed as:
df = (num of columns - 1)(num of rows - 1) = (5 - 1)2 = 16

Therefore, for 0.025 level of significance, we get from the chi square distribution tables here:

Therefore 28.9 is the critical value here.

As the critical value here is lower than the chi square test statistic value, therefore the chi square test statistic value lies in the rejection region and we can reject the null hypothesis here.

b) The degrees of freedom here is computed as:
df = (num of columns - 1)(num of rows - 1) = (6 - 1)*(7 - 1) = 30

For 0.1 level of significance, we get from the chi square distribution tables here:

Therefore 40.3 is the required critical value here.

As the given critical value here is equal to the test statistic value, therefore we can reject the null hypothesis here and the test is significant here.