Small totals favour a smaller exponential mean; $2T/\theta_0\sim\chi^2_{2n}$

Let $X_1,X_2,\dots,X_n$ be iid random sample of size $n$ from exponential distribution with mean $\theta$. The MP test of size $\alpha$ for testing $H_0:\theta=\theta_0$ against $H_1:\theta=\theta_1<\theta_0$ is ($T=\sum X_i$):