"I do not study."
Translation:저는 공부하지 않습니다.
To negate a verb or an adjective there are two forms of negation, long form and short form negation. We discuss negation with 안. 안 is a contraction of "no" / 아니. This explanation does not discuss negation with 뭇 (cannot) which can also be used in long and short form negation.
Short form negation: 안 + inflected verb
안 가요 (do not go)
안 배워요 (do not learn)
안 마셔요 (do not drink
Verbs and adjectives that already have a corresponding negation can not be used with short form negation. Example: 모르다 (to not know).
If the verb is a compound verb, then the short form negation will change. Compound verbs are of the form "noun + 하다". Recall that 하다 is the uninflected verb "to do".
Short form negation with compound verb: noun + 안 + 하다 inflected
키스 안 해요 (do not kiss)
수영 안 해요 (do not swim)
공부 안 해요 (do not study)
Long form negation: stem + 지 않다 inflected
먹지 안아요 (do not eat)
마사지 안아요 (do not drink)
비싸지 안아요 (is not expensive)
공부하지 않아요 (do not study)
Note that long form negation does not change when used with a compound verb.
So when does one use short form or long form negation?
Quoted from Basic Korean (Andrew Sangpil Byon):
"There is no meaning difference between the long form negation and the short form negation. Consequently they are used interchangeably. However, the long form negation tends to be more often used in written and formal communication."
Unit 18 of the aforementioned book exhaustively discusses negation in Korean language.
This is not grammatically correct. Short form negation when used with a compound verb like 공부하다 is different than short form negation with a non-compound verb, see my answer.
It probably marked it correct because the omission of the object particle 을 / 를 is acceptable in Korean language, though more informal. You placed a space between 공부 and 합니다. The following statement is grammatically correct: 저는 공부를 안 합니다
It's not correct to write 저는 안 공부합니다. 공부하다 is a compound verb. In compound negation with 안, the inflection of 하다 is placed after 안 as in 저는 공부 안 합니다.