<p>Many linguists over the years have objected to “hopefully” when used in place of “I hope.” Their argument is that “hopefully,” as in “Hopefully, I will be accepted,” acts as an adverb and therefore must modify a verb: “I will be accepted in a hopeful manner.” This clearly does not mean “I hope I will be accepted.” However, adverbs can describe general situations and tones portrayed in the entire clause, rather than a specific verb, as in these examples:
“Frankly, this soup is not tasty.” (This can’t logically mean “This soup is not tasty in a frank, honest way.” Rather, the placement of the adverb suggests something about the speaker, that he or she is being frank.)</p>
<p>“Sadly, the man died.” (The way in which the man died is not necessarily sad: the situation involving his death is sad, or the speaker is making the statement in sadness.)
So it might be more clear to use “I hope,” but “hopefully” is acceptable, popular, and standard as a replacement.</p>