The word "hypothesize" means to put forward a tentative explanation for something, based on available evidence, and without having all the facts. Therefore, the word that is most nearly the opposite in meaning to "hypothesize" is option A, "refute."

When someone "hypothesizes," they are making a guess or conjecture about something based on limited information. To "refute," on the other hand, means to prove something false or incorrect, so it is the opposite of hypothesizing.

Option B, "conjecture," means a guess or theory based on incomplete information, which is similar to "hypothesize." Option C, "posit," means to put forward an idea or theory as a basis for argument or discussion, which is similar to "hypothesize." Option D, "speculate," means to make an educated guess about something, which is also similar to "hypothesize." Therefore, A is the best choice as the opposite of "hypothesize."