SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 559 



For example, on the basis of past experience the experimenter may 

 estimate that the probabilities associated Avith his k = 4 processes are 

 all in the neighborhood of 0.60. This constitutes his a priori knowledge. 

 He may then decide that he would like to make a correct selection 

 with probability P* = 0.85 when the best process has a yield of at least 

 75 per cent and all the others have a yield of at most 60 per cent. Enter- 

 ing column 1 of Table VII we find that n = 45 observations per process 

 are required. 



It is much more difficult to furnish tables for the alternative specifica- 



Fig. 16 — Number of units required per process to guarantee a probability of 

 P* of selecting the best of four binomial pi-ocesses when the true pm ^ p*i| and 

 the true p(2i ^ p[2) . 



