  The conventional model of disjunctive group testing assumes that there are
several defective elements (or defectives) among a large population, and a
group test yields the positive response if and only if the testing group
contains at least one defective element. The basic problem is to find all
defectives using a minimal possible number of group tests. However, when the
number of defectives is unknown there arises an additional problem, namely: how
to estimate the random number of defective elements. n this paper, we
concentrate on testing the hypothesis $H_0$: the number of defectives $\le s_1$
against the alternative hypothesis $H_1$: the number of defectives $\ge s_2$.
We introduce a new decoding algorithm based on the comparison of the number of
tests having positive responses with an appropriate fixed threshold. For some
asymptotic regimes on $s_1$ and $s_2$, the proposed algorithm is shown to be
order-optimal. Additionally, our simulation results verify the advantages of
the proposed algorithm such as low complexity and a small error probability
compared with known algorithms.
