Based on the current understanding of this operon, which hypothesis would be useful for james to test ?

The answer is Addition of allolactose to the bacterial growth media should increase the speed at which the bacteria metabolize the sugar lactose.

The lac operon is a group of genes transcribed together that code for the transport and metabolism of lactose (lac). It is present in many bacteria.

In the lac operon, allolactose binds to and deactivates Lacl. Since LacI is the repressor of the lac operon genes, its deactivation allows the lac operon transcription. Transcription, and consequently translation, result in synthesis of proteins required for lactose metabolism. 
Therefore, addition of allolactose to the bacterial growth media will activate lac operon, and thereby should increase the speed at which the bacteria metabolize the sugar lactose.

C) reflection (i also looked up the other choices just to make sure)