### Abstract:

In this paper computer simulation is employed to investigate
the nature of the error sizes and the distribution of sample size
required in a sequential probability ratio test (SPRT). In the
test we can distinguish between two kinds of error probabilities.
The first kind are the specified error probabilities which are
usually denoted by a and B, and the second kind are the true
error probabilities which may be denoted by at and Bt• Wald has
shown that the relation at + Bt ~ a + B holds true. The objective
of this project is to investigate the relation between at and a,
and between Bt and B. As sample size required in SPRT is a random
variable, its distribution is also studied. Two probability
distributions: Bernoulli and normal (known variance) are selected
for the study.
The study shows that in ,t.he' case 'of norma'l' distribution,
when the parameters under rio:: 5rrd' :~i' ;~re: ,sl~g~~i~ :f*~: :*p,~'tt and
a = B, the estimates of true error, 'probahiIi ties, C',1:'e less 'than
their corresponding specifi~d ~rror i)r('b~hi!iit~es and"that 'they
are close to each other. The est:lmat,es ~t ;t' 'a'h? ~t ,~1~9 decr:ease
as d = 9 1 - 90 increases. Th~s, lillJ.q~s, t~a,t, tlJ.~ ~9t~a,i ~iflks, {iz:e by
far less than the specified value for large d. When a and Bare
not equal, there are times when the estimate of at or Bt exceeds
its corresponding specified error size as observed. But, still
if the parameters under HO and HI are far apart, the estimates
indicate that at ~ a and Bt ~ B.
For Bernoulli distribution, the results are not very far
from those of normal except that in some cases the estimates of
at or Bt are found to be greater than a or B which led to
disobeying the inequality at + Bt ~ a + B. This may be attributed
to sample fluctuation.
And finally, sample size distribution is observed to depend
mainly on d = 9 1 - 9 0 (90 < 9 1). The mean and variance of the
required sample size increase rapidly as d decreases. Further,
the distributions are all positively skewed. It is also observed
that in rare occasions there is a chance that the sample size in
SPRT exceeds the size one needs in non-sequential test