Consider a two-way contingency table with three rows and three columns. Suppose that. for i = 1, 2, 3, and j = 1, 2, 3, the probability Pi} that an individual selected at random from a given population will be classified in the ith row and the ith column of the table is as given in Table 9.12
(a) Show that the rows and columns of this table are independent by verifying that the values Pj satisfy the null hypothesis Ho in Eq. (5).
(b) Generate a random sample of 300 observations from the given population by choosing 300 pairs of digits from a table of random digits and classifying each pair in some cell of the contingency table in the following manner: Since PI I = 0.15, classify a pair of digits in the first cell if it is one of the first fifteen pairs 01, 02, . . . , 15. Since PI2 = 0.09, classify a pair of digits in the second cell if it is one of the next nine pairs 16,17, ... , 24. Continue in this way for all nine cells. Thus, since the last cell of the table has probability pJ) = 0.08, a pair of digits will be classified in that cell if it is one of the last eight pairs 93, 94, ... , 99,00.
(c) Consider the 3 X 3 table of observed values Ni} generated in part (b). Pretend that the probabilities Pi} were unknown, and test the hypotheses (5).
Table 9.12
