Tell them it will be impossible for anything to go wrong, as you will be having all-night parties until they get back. 
Having been in that situation before, I find it best to turn on a radio or something, give some good ‘white noise’, in case you are, in fact, creeped out by being alone.
First time I got left ‘home alone’ it was so that the rest of my family could go to Disneyland..“Oh.. you can’t go? Well, that’s ok.. we needed someone to watch the house..“
I *really* hate my stepmother, since she deliberately planned the trip for when I was taking mid-terms. Found out later that she had told my dad I’d said I didn’t want to go.