Suppose we are testing $H_0: \theta = \theta_0$ against $H_1: \theta \neq \theta_0$ using the Likelihood Ratio Test. If $\Lambda = \frac{L(\theta_0)}{L(\hat{\theta})}$ is the likelihood ratio, which statement accurately describes the asymptotic behavior of the statistic $T = -2 \ln \Lambda$ as the sample size $n$ tends to infinity?