The noun conjecture means an opinion that is not based on proof but on how it seems.
Synonyms are guesswork, hunch, hypothesis, or inference.
The word origins from Old French (late 14th century) conjecture meaning “surmise, guess”, or directly from Latin coniectura meaning “conclusion, interpretation, guess, inference”, past participle of conicere meaning “to throw together”. It comes from com meaning “together” plus iacere meaning “to throw”. The sense of “an unverified supposition” is from 1520s.
She saw a lot of conjecture in the news about her pregnancy.
The neighbors gave conjecture to the reporters about the exact cause of the fire.
Her friends believed her conjecture on their exam.