Question 1120532
These are two independent samples from a population.
Use a t-test for independent samples.
Because one is not looking at each family with monetary and non monetary incentives, a dependent sample would not be used.  One does not know the parameters, so a z-test would not be used.
Correlation could be done but would not be nearly as useful.

What is bothersome is how drought is determined.  If this were in a drought, then the study would answer the question.  If one were thinking to measure this in normal times, then 3 months would not be enough time to know whether there was a drought.