Translation:Did the prime minister choose her new government?
Yes, and "sin" can never be in the subject of a sentence. Another hint that it applies to "regjering" is because "nye" is in the "plural/defined" form of the adjective, which indicates us that "sin" refers to "regjering" making it "definite". I'm sorry if this was too confusing... I never know the exact grammatical definitions.
AnaSrsh, you're correct that statsministeren is the subject and that sin cannot be in the subject but you have forgotten the sentence is a question and that there has been a subject and verb inversion. The declarative sentence from which the question arises is "Statsministeren valgte sin nye regjering". From which you can see that 'sin' refers back to the subject.
Your reply in this thread was written quite some time ago so my above comment is possibly of little value to your ongoing learning now. I am only responding here largely to assist later readers of this thread and not to criticize your knowledge or understanding.
How do we know that the prime minister is female from this sentence? And why is 'has ...chosen" not accepted? Even though the construction with "har" is not used in the Norwegian, "has chosen" is what would normally be used for this question in English. "Did" allows the possibility that someone else could have chosen the government, i.e. the monarch, or the minister for fish, or...has she actually done it yet? It is, in any case, emphatic. Does the Norwegian here have any suggestion of emphasis?
We don't know whether the prime minister is male or female, both translations are correct. The "har" construction is used in Norwegian, and that would be "Har statsministeren valgt sin nye regjering?".
Besides that, I don't really understand how the phrase could be ambiguous as you stated... "Did the prime minister choose" and "has the prime minister chosen" leave no ambiguity for the subject; at least none that I can imagine.
"has chosen" is what would normally be used for this question in English.
Unless you are asking about something which happened in, say, 2013. It is something that is rather implied by the chosen tense form than is expressed directly. Something similar to the subtle distinction between
I haven't seen her this morning. (it is still this morning)
I did not see her this morning. (the conversation takes place in the evening/at midnight etc., the morning is over)
And it is not "X did choose Y", it is "did X choose Y?". The former is the emphatic form while the latter is just a question.
That's the way I see it. Don't take my word for it, though. Since I am not a native English speaker.
As for emphasis in sentences, I haven't reached that chapter yet, but here is an excerpt from what is said in one of the Norwegian grammar books that I have:
Utbryting bruker vi først og fremst for å framheve et ledd i en setning.
I presenssystemet begynner en utbryting slik: Det er ...
I preteritumsystemet begynner en utbryting slik: Det var ...
Etter utbrytingen får vi en som-setning. En som-setning er alltid leddsetning.
Vi kan bryte ut alle ledd i en setning (unntatt verbal). Hvis vi bryter ut subjektet, må vi bruke som etterpå. Leddet som brytes ut, får trykk når vi snakker, og vi presiserer det ofte som en motsetning til noe annet. Utbryting brukes mest muntlig.
Jon skal reise til Bergen i morgen.
Det er Jon som skal reise til Bergen i morgen, (ikke Per)
Det er til Bergen Jon skal reise i morgen. (ikke til Stavanger)
Det er i morgen Jon skal reise til Bergen. (ikke en annen dag)
I agree with Deyan161 that the English sentence as presented has some sinister overtones in that it implies that someone other than the prime minister is doing the choosing.
I understand your comment that if we were talking about some time in the past then we would say 'did he choose' but I can't think of an example in English where the pertinent time would not also be part of the question. And even then, with this particular subject, it still sounds more like we're questioning whether it was the prime minister or some other agency who did the choosing rather than simply asking whether the government had actually been chosen (the lack of total anarchy implies it was).
Having said all that, I can see why 'has chosen' is not accepted because it is a slightly different tense, it's just that the direct English translation takes on some massive overtones that are not there in the Norwegian - or maybe they are? The random and fun questions our course creators pose are one of the reasons this is my favourite Duo course :)
den nye regjeringen sin but
sin nye regjering.
Look here https://www.duolingo.com/skill/nb/Adjectives/tips-and-notes
The section "Combining Possessive Pronouns with Adjectives"