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 pij that an individual selected at random from a given population will be classified in the ith row and the jth column of Table 10.20.
Table 10.20 Data for Exercise 7

a. Show that the rows and columns of this table are independent by verifying that the values pij satisfy the null hypothesis H0 in Eq. (10.3.3).
b. Generate a random sample of 300 observations from the given population using a uniform pseudo-random number generator. Select 300 pseudo-random numbers between 0 and 1 and proceed as follows: Since p11 = 0.15, classify a pseudo-random number x in the first cell if x c. Consider the 3 × 3 table of observed values Nij generated in part (b). Pretend that the probabilities pij were unknown, and test the hypotheses (10.3.3).

0.15 0.09 0.06 0.15 0.09 0.06 0.20 0.12 0.08