I would never pay $15 for a babysitter, and I have 6 kids.
I'm speaking of rates in Denver, CO.
Rates vary based on WHO is babysitting. The 14 year old neighbor, or a certified adult from a service? (Check out nanny websites in the town your story is set in to get a rough idea of those rates.)
What is the sitter expected to do? Watch the kids, or be a "mom" - cleaning, cooking, laundry too?
Is it one night or every day/nanny type? Are the kids older, or babies with feeding and diapers?
I paid my nanny, a 19 yr. old part time college student, $400/week (5 days). I had a newborn, a 2 yr. old, and a 3 yr. old at home all day, and then a school age son (7) for 1 hour per day (4pm-5pm).
When I hired the 14 yr. old from church to watch the kids for a movie night, I paid her $7.50 for 5 kids (there were diapers, but they were also asleep for a good part of the time.)
Another good resource is to check out the Craigslist ads for the target city. Rates do vary geographically - $7.50/hr. where I am now is outrageously high.
Pretty much, whenever I ask a teenager how much, they don't have a clue either. I usually let their mom know $5/hr, $30 for the evening, or whatever so I know it's okay. Also, keep in mind if the sitter will provide transportation or will have to be picked up and dropped off.