Summary: Let \(X\) be a random variable with negative binomial density \[ f \bigl(x \mid \theta\bigr) =\left[ {\Gamma (x+r) \over\Gamma (x+1)\Gamma (r)} \right] \theta^x (1-\theta)^r, \] where \(x=0,1,2, \dots, 0<\theta <1\), \(r>0\). For the hypothesis testing problem \[ H_0: \theta\leq \theta_0 \quad\text{versus} \quad H_1: \theta> \theta_0 \] 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.