For a population of athletes, each independently has a probability p of using steroid. If p is smaller than a special p-value p*, then it is more efficient to do pairwise group testing of the samples than to test the samples one at a time. p* is found to be approximately 0.38.
Problem: Two population of athletes with different p values p1 and p2 both of whom are assumed to be less than p*. Assuming that p1<p2, is it more efficient to test the two populations separately or to test one of each together? What do you do if the joint sample is positive?
Please see the attached file.
i). If the two population is tested ...
This solution calculates the efficiency of testing two populations vs. one.