In order to determine the correct answer to this question, we must first define the word "optimistic."
The word optimistic means positive, cheerful, or upbeat. In other words, it means HOPEFUL. On the other hand, if the author felt hopeless about a character or situation, the tone would instead be pessimistic, or negative.
For example, if an author described a character waking up in the morning with a smile, the tone would be an optimistic one. If the character woke up in the morning and pulled the covers back over his head, refusing to get out of bed, then that would imply a hopeless tone.
A character who refuses to be defeated and keeps fighting against the odds would illustrate the author's optimism. If, however, the character cried and whined at every problem, the tone would be a pessimistic one.
Therefore, the above statement is false. A writer who wanted to convey an optimistic tone would use words that would indicate he or she felt HOPEFUL. Because this sentence instead uses "hopeless," this statement is false.