  In this paper we study a new, generalized version of the well-known group
testing problem. In the classical model of group testing we are given n
objects, some of which are considered to be defective. We can test certain
subsets of the objects whether they contain at least one defective element. The
goal is usually to find all defectives using as few tests as possible. In our
model the presence of defective elements in a test set Q can be recognized if
and only if their number is large enough compared to the size of Q. More
precisely for a test Q the answer is 'yes' if and only if there are at least
\alpha |Q| defective elements in Q for some fixed \alpha.
