Translation:About thirty guests are in the hotel.
albergo seems to be one of those words, similar to in cucina, in bagno, in casa, in tavola (as opposed to sul tavolo) ecc, where the "the" is incorporated in the word itself. From what I can deduce, it seems to apply to places, rooms, ecc. for which there is a specific name. So, for example, "camera del letto" is "room of the bed" so it still uses the article. But "cucina" is the name for "room where one cooks" and therefore has a specific name and follows the construction without the extra article. It is very tricky to know which nouns follow this rule, and I would love to see a list of them. So far, I've been "meeting" the special noun, getting the answer wrong once or twice, and then finally remembering that it's one of the "special" ones...
First of all it would be "nell'albergo" because albergo starts with vowel.
Anyway by using nel (in + il) so a preposition plus a determinative article you would be referring to some specific thing.
Explanation: 1- I'm at the hotel Sono in albergo
2- I stayed at the hotel you had told me about Sono stato nell'Hotel di cui mi avevi parlato
Many others work like this in ufficio, in stazione, in classe, in bagno, in cucina, in aeroporto
Hope this helps!
It doesn't help that originally "hostel" and "hotel" were the same word, the latter corrupted through the French hôtel; and moreover they're probably from an ancient corruption of "hospital" or "hospice". Regardless, they are different words nowadays, and as Viaggiatore pointed out hostel is "ostello" and hotel is "albergo" (or simply hotel, the loanword is very popular).
Some of you using "nell'albergo", using this is perfectly fine and grammatically correct, it's just that this is a listening exercise and the woman says "in albergo", which is also correct (a more generalised version, like the difference between saying "I eat fish" and "I eat the fish". Both are fine, just suit a particular situation more than the other depending on context).