Why do employers ask how much you are expecting to be paid?

So I made a mistake yesterday while filling out an application. Minimum wage in my county is 10.75 and I applied for a caregiver position and said I wanted to be paid 11.00. However most caregiving jobs around me are paying 13.00 and over. I wrote down I wanted to be paid 11.00. Does that mean they will be paying me 11.00 because I asked for it? I do have experience doing that job so I should have asked for more I feel like. I feel like I sold myself short.