Statistical Inference — critical constant of a normal-mean LRT

Consider a random sample $\{x_1, x_2, x_3, x_4\}$ from $N(\mu, \sigma^2)$ distribution. Define $\bar{x} = \frac{\sum_{i=1}^{4}x_i}{4}$ and $S^2 = \frac{\sum_{i=1}^{4}(x_i - \bar{x})^2}{3}$. The LRT of size $\alpha = 0.05$ rejects $H_0 : \mu = 0$ versus $H_1 : \mu \ne 0$ if and only if $\frac{|\bar{x}|}{S} > k$. The value of $k$, when $P(X > t_{(n,\alpha)}) = \alpha$, is