8. An experiment with n observations XI" '" Xn is planned, with each X; distributed as N(8,1). However, some of the observations do not materialize (for example, some of the subjects die, move away, or tum out to be unsuitable). Let Ij = 1 or 0 as is observed or not, and suppose the Ij are independent of the X's and of each other and that P(Ij = 1) = p for all j. (i) If p is known, the effective sample size M = "i.lj is ancillary. (ii) If p is unknown, there exists a UMP unbiased level-a test of H: 8 s 0 vs. K : 8 > D. Its conditional level (given M = m) is am = a for all m = D, ... , n.