Let X be a random variable with negative binomial density $$ f(x|\theta)=\displaystyle{\Gamma (x+r)\over \Gamma (x+1)\Gamma (r)}\theta^x(1-\theta)^r, $$ where $x=0, 1, 2, \cdots , 0 \lt \theta \lt 1,~r \gt 0$. For the hypothesis testing problem $$ H_0 : \theta \leq \theta_0~~~~{\rm versus}~~~~H_1 : \theta \gt \theta_0 $$ based on observing X$=x$, where $\theta_0$ is specified, we consider it as an estimation problem within a decision-theoretic framework. We prove the admissibility of estimator $p(x)= P_{\theta_0}(X \geq x)$, the $p$-value, for estimating the accuracy of the test, $1_{(0,\theta_0)}(\theta)$, under the squared error loss.