Make her tell your parents. If you tell them, you'll look like a tattletale. Make her tell them. If she is old enough to be sleeping with boys, then she is old enough to admit it to her parents.
In any case, your parents ought to know. If you sister is sleeping with someone ( or someones), she is susceptible to STDs and all sorts of trouble that comes along with that nonsense. Even if she ends up not being pregnant, it still might not scare her off from doing it altogether. Children as young as that should not be sleeping with anyone, period.
take a pregnancy test. There is most likely a free clinic somewhere in your town... they will give free tests. also if the test comes back negative she can get free birth control at the free clinic as well... (and you don't need a parents permission!)
words of advice... You sister is 16 she should NOT be having sex! Neither should YOU unless you are making LOVE to your husband!!
Get her a pregnancy test. Then make sure she tells your parents what is going on no matter what the outcome of the test. If she is pregnant she needs to see a doctor. If she isn't pregnant she still needs to see a doctor and get on birth control.
First, tell your percents, they are going to know soon enough. Second, tell ALL you know about the boyfriend she's with. Third, be prepared for her anger, she's going to be very angry you broke her trust. Sadly too many teens destroy their lives with unplanned pregnancy. Its going to change her life, and everyone she'll need to help her through this. Pray its not true, but prepare for the worst! Hopefully your parents, when they get this wake up call, will heed the risks their child is taking, and take appropriate action to see it doesn't happen again till she's ready to take responsibility for her own actions.
Who's older, you or her? You're question was to believe her or not, right? Everyone has already given you great advice on what to do, so I need not bother. I'll just answer your question. If she's older then you, she may be testing you to see if you can keep a secret or not. Get a pregnancy test kit and tell her you want to see the proof. Then if she is really pregnant, I would tell her you have to share this info with your parents. Offer to sit with her while she tells your parents. If she's pregnant, she's going to need all of your help and support. You can start supporting her by being with her when she talks to your parents. That way she knows she can trust you. Good luck to your whole family. Kids having kids, going to need all the luck you can get.