43. Consider the third of the three sampling schemes for a 2 X 2 X K table discussed in Chapter 4, Section 8. and the two hypotheses HI: iii = . .. = Ii K = 1 and Hz: iii = . . . = Ii K • (i) Obtain the likelihood-ratio test statistic for testing HI' (ii) Obtain equations that determine the maximum-likelihood estimates of the parameters under Hz. (These equations cannot be solved explicitly.) (iii) Determine the number of degrees of freedom of the limiting xZ-distribution of the likelihood-ratio criterion for testing

(a) HI'

(b) Hz. [For a discussion of these and related hypotheses. see.for example Shaffer (1973), Plackett (1981). or Bishop. Fienberg, and Holland (1975). and the recent study by Liang and Self (1985).]