For metallic structures, does the packing efficiency (see sample exercise 12.1 in textbook) increase or decrease as the number of nearest neighbors (the coordination number) decreases?

Metallic solids or metallic structures experience metallic bonds which are the forces of attractions between the sea of electrons and the nucleus of the metallic atoms. They share a network of highly delocalized electrons.
I therefore think that the packing efficiency decreases as the number of nearest neighbors decreases.

Which of the following did you identify correctly

There is no reason to think the results are biased or not conducted properly but you should not assume the results are correct just because they were done in a laboratory so the answer would be c. it is likely to be reliable because the results support the conclusion presented.