Critical value of a Gaussian LRT

Let $x_1,x_2,x_3,x_4$ be the observed values of a random sample from a $N(\mu,\sigma^2)$ distribution, where $\mu\in\mathbb{R}$ and $\sigma\in(0,\infty)$ are unknown parameters. Let $\bar x$ and $s=\sqrt{\frac13\sum_{i=1}^4(x_i-\bar x)^2}$ be the observed sample mean and the sample standard deviation, respectively. For testing $H_0:\mu=0$ against $H_1:\mu\neq 0$, the likelihood ratio test of size $\alpha=0.05$ rejects $H_0$ if and only if $\frac{|\bar x|}{s}>k$. Then the value of $k$ is