I'd love to know at what age people think it is safe to leave a child home alone?

My oldest daughter is 13 and many of her friends spend long periods at home alone, particularly in the school holidays when their parents work. 

We have only recently left her in the house for 20-30minutes while I run a local errand. Am I being over cautious? 

Also at what age would it be ok to let her watch her younger siblings (aged 8+10) She says lots of her friends do this and she said she wants to have a try. She is trying to talk us into having a date night at a local cafe 4 minutes down the road. 

I would really love to hear other mothers opinions,

Thanks, Gina.