An inference
a. is a possible explanation for events using prior knowledge
b. explains if a hypothesis is or is not valid
c. is made independent of observation or prior knowledge
d. can be either qualitative or quantitative

a student conducts an experiment to determine how the amount of water given to a plant affects its growth.
which of the following is not a control for this experiment?
a. the type of plant
b. the amount of soil
c. the amount of water
d. the amount of time

The answer to your first question is A - A possible explanation for events using prior knowledge.

Inferring something from data means that we're making a possible explanation for something with using our prior knowledge. 

To answer your second question - the question is stated in a weird way. It could either be B - the amount of soil od D - amount of time. For neither of those does it mention whether or how does the student take them into account. 

I would go with D in the second question however. 

Yes he did ; ) hope that