  This paper studies one-sided hypothesis testing under random sampling without
replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$
are subject to a permutation invariant distribution and $n$ binary random
variables $X_1,\ldots, X_{n}$ are observed, we have proposed randomized tests
with a randomization parameter for the upper confidence limit of the
expectation of the $(n+1)$th random variable $X_{n+1}$ under a given
significance level $\delta>0$. Our proposed randomized test significantly
improves over deterministic test unlike random sampling with replacement.
