Pooling contingency tables can produce spurious association. A large organization is being investigated to determine if its recruitment is sex-biased. Tables 15 and 16, respectively, show the classification of applicants for secretarial and for sales positions according to gender and result of interview.
Table 17 is an aggregation of the corresponding entries of Table 15 and Table 16.

(a) Verify that the x2 statistic for testing independence is zero for each of the data sets given in Tables 15 and 16.
(b) For the pooled data given in Table 17, compute the value of the x2 statistic and test the null hypothesis of independence.
(c) Explain the paradoxical result that there is no sex bias in any job category, but the combined data indicate sex discrimination

TABLE 15 Secretarial Positions Offered Denied Total Male Female 75 Total 75 225 25 50 150 100 200 300 TABLE 16 Sales Positions Offered Denied Total Male Female 150 75 50 25 75 200 100 Total 225 300 TABLE 17 Secretarial and Sales Positions Offered Denied Total 275 Male Female150 Total 175 100 175 275 325 325 600