Haar transform definition
The only difference between the two transform results is a gain factor.  The transform should have the same energy as the original data sequence, so we can use that to check for the right result.  The energy of $X$ is-

$$
\sum X^2 = 484
$$
$$
\sum (5,9,11,3,−1,−1,2,0)^2 = 242
$$
$$
\sum (\sqrt{2}(5,9,11,3,−1,−1,2,0))^2 = 2\sum (5,9,11,3,−1,−1,2,0)^2 = 484
$$
This shows that of the two possible transforms, $\sqrt{2}(5,9,11,3,−1,−1,2,0)$ has the right energy and is thus the right choice.