  We consider sequential hypothesis testing based on observations which are
received in groups of random size. The observations are assumed to be
independent both within and between the groups. We assume that the group sizes
are independent and their distributions are known, and that the groups are
formed independently of the observations.
  We are concerned with a problem of testing a simple hypothesis against a
simple alternative. For any (group-) sequential test, we take into account the
following three characteristics: its type I and type II error probabilities and
the average cost of observations.
  Under mild conditions, we characterize the structure of sequential tests
minimizing the average cost of observations among all sequential tests whose
type I and type II error probabilities do not exceed some prescribed levels.
