All 3 Uses

hypothesis
in
Mountains Beyond Mountains
(Edited)

He'd tell the story of how, early in the aids epidemic in the United States, sociologists and even medical people had hypothesized that HIV had come from Africa to Haiti, then to the United States.
Chpt 2.11 *

hypothesized = proposed a seemingly reasonable, but unproven, idea

standard suffix: The suffix "-ize" converts a word to a verb. This is the same pattern you see in words like apologize, theorize, and dramatize.
Some experts even hypothesized that the disease had originated in Haiti, where, it was said by some, Voodoo houngans ripped the heads off chickens and guzzled their blood, then had sex with little boys.
Chpt 2.11
I began to pose a hypothetical question, which I thought expressed great insight into his peripatetic life.
Chpt 4.23 *

hypothetical = imagined for discussion

Definitions:

(1) (hypothesis as in: a study to test her hypothesis)
a seemingly reasonable, but unproven idea or explanation based upon known facts

In casual conversation, theory is a synonym for hypothesis, but a scientist would say that a hypothesis needs to pass rigorous tests before it could be accepted as a theory.
(2) (hypothesis as in: assume as a working hypothesis)
something that may or may not be true, but is temporarily treated as true to advance a discussion or to further investigation

This sense of hypothesis is typically seen in the form, hypothetical, or hypothetically.
(3) (meaning too rare to warrant focus)