<p>
Just to clarify, the SAT will not mark a sentence like Hopefully, the man will be punished wrong: it considers this usage right, not wrong. The SAT accepts sentence adverbs as grammatical. If “hopefully” was an answer choice in that context in the identifying errors section, it would not be the answer (it would be viewed as grammatical). If, however, “hopefully” is clearly being used as a traditional adverb, as in The man will be punished hopefully, without a comma before “hopefully,” keep in mind that the sentence’s meaning changes (but isn’t necessarily illogical). The comma (e.g., in Unfortunately, . . .) is essential to the sentence adverb.</p>
<p>In the wider scope of things, introductory adverbial/prepositional phrases (a la the sentence adverb) are very relevant on the SAT, and you should understand what modifies what.</p>