Answer
The parallax angle of the farther star will be smaller than that of the nearer star by a factor of $2$.
Work Step by Step
We can use this equation to find the distance D to the star:
$D=\frac{d}{\phi}$, where d = 1 AU and $\phi$ is the parallax angle.
If $D_2 = 2~D_1$, let's compare $\phi_2$ and $\phi_1$.
$\phi_2 = \frac{d}{D_2} = \frac{d}{2~D_1} = \frac{d}{2d/\phi_1} = \frac{\phi_1}{2}$
Therefore the parallax angle of the farther star will be smaller than that of the nearer star by a factor of $2$.
