Hi I need help with the following question.

Tests of independence and homogeneity, which are performed using contingency tables. We may have information on more than one variable for each element. Such information can be summarized and presented using a two-way classification table, which is also called acontingency tableorcross-tabulation.

A contingency table can be of any size.In atest of independencefor a contingency table, we test the null hypothesis that the two attributes (characteristics) of the elements of a given population are not related (that is, they are independent) against the alternative hypothesis that the two characteristics are related (that is, they are dependent).

We perform such a test by using the chi-square distribution.The null hypothesis in a test of independence is always that the two attributes are not related. The alternative hypothesis is that the two attributes are related.The frequencies obtained from the performance of an experiment for a contingency table are called theobserved frequencies. The procedure to calculate theexpected frequenciesfor a contingency table for a test of independence is different from the one for a goodness-of-fit test.

Now, as you are so fond of always answering, can we frame this using realistic, everyday scenarios?Where would we use all this stuff?Thoughts?