What is the value of gravitational acceleration at a distance of half the earths radius above the earths surface?

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Correct. For a sphere of uniform density, the acceleration drops off linearly. $$g = g_{surface} \frac{r}{R}$$ where $r$ is the location under consideration, $R$ is the radius of the sphere and $r < R$.

Under such a scheme, gravity would be one half that at the surface.

The earth is not a uniform sphere though. The outer crust is much less dense than the iron core. Approaching this core then allows gravity to increase with depth for a distance before finally decreasing.

The Gravity of Earth wiki page has a graph based on a reference model of the density of the earth with depth.

Under that model, gravity at half the earth's radius is just about equal to that at the surface.