Likelihood ratio test — a one-sided test for an exponential scale

Let $X_1,X_2,…,X_{15}$ be a random sample from an Exponential distribution with the probability density function $f(x\mid\sigma)=\frac1\sigma\exp\left(-\frac{x}{\sigma}\right)$ for $x>0$ and 0 elsewhere, where the unknown parameter $\sigma$ is positive. Let $\bar X=\frac{1}{15}\sum_{i=1}^{15}X_i$. Suppose that $\phi$ denotes the likelihood ratio test for testing $H_0:\sigma\le1$ against $H_1:\sigma>1$ at level $\alpha=0.1$. It is given that $\chi^2_{15,0.1}=22.307$, $\chi^2_{15,0.9}=8.547$, $\chi^2_{30,0.1}=40.256$, $\chi^2_{30,0.9}=20.599$, where $\mathbb{P}(W>\chi^2_{n,\alpha})=\alpha$ and $W\sim\chi^2_n$. Then which of the following statements are true?