Translation:I also do not have a younger sister.
不 bù - no : used with the verb - to be 是 shì or other verbs in the present or future tense. When placed before a verb, preposition or adverb it negates the action.
没 méi - not, none: is used with 有yǒu - to have (méiyǒu 没有 - hasn't, haven't, didn't, does not have, there is not, be without)
The phrase "as well" is used to denote the addition of something to other something(s). It doesn't work to indicate an absence or deficit, not even to indicate an absence or deficit of something that happens to be the same absence/deficit as someone else has in common with another.
The word that is used to indicate a lack or deficit of something, even if it's in common with someone else's lack or deficit is one of either or neither. The correct Choice depends on exactly what you need to say.
In this case, then, the correct answer would then be "I don't have a younger sister either."
In some of the courses, you have such an option. For example, in the French course, you can click on "Words" between "Home" and "Discussion" in the blue banner at the top of the screen to open a list of the words you have seen, when you last practiced them, and so forth. However, I do not think the Chinese course has such an option at this time, 26Mar2019. Making your own list, using a text document or old fashioned notebook or note cards and pencil, might actually be more helpful.
My translation "I do not have a younger sister, also." I know in Chinese we can't place "also" at the end of the sentence, but in English this isn't a problem. Seeing as my translation arrives at the same meaning, should it be counted as correct? I think so. What do you think fellow duolinguists?
Right! It is best to remember 有 (to have/there is) and 没有 (to have not, there is not) together. It is always 没有. You will encounter it so often that it is really easy to remember after a while.
You will also encounter the 没 without the 有, but that is mostly only when the 有 can be omitted. (For instance: 我没想到…… = I would never have thought ...)