During the serological test in which anti-human serum is mixed with the blood of another animal, the blood of this animal gives the thickest precipitate

The correct option is chimpanzee.

This question is based on the principles of serology and evolutionary relationship studies, specifically precipitin tests (or antigen-antibody reaction tests) used to determine phylogenetic proximity between species.

When human blood serum (containing human proteins) is injected into another animal, such as a rabbit, the rabbit's immune system produces antibodies against the human proteins. This serum containing anti-human antibodies is called anti-human serum.
When this anti-human serum is mixed with the blood serum of other animals, the anti-human antibodies react with the serum proteins of those animals. The antibodies bind to similar proteins (antigens) and form a visible precipitate. The thickness or amount of this precipitate is directly proportional to the structural similarity of the serum proteins between the two species.

Since proteins are synthesized based on genetic code, greater similarity in protein structure indicates a closer evolutionary relationship and a more recent common ancestor.
Among the options provided:
1. Chimpanzees share the highest percentage of genetic similarity and the most recent common ancestor with humans.
2. Gibbons are apes but are evolutionarily more distant than chimpanzees.
3. Dogs and mules (which are hybrids of horses and donkeys) are non-primate mammals and are evolutionarily much more distant from humans than chimpanzees or gibbons.

Therefore, the blood proteins of the chimpanzee react most strongly with the anti-human serum, resulting in the thickest precipitate due to their close evolutionary proximity to humans.