['My kids have been begging me to let them stay home alone without a babysitter while I work. They are old enough now I guess.', "Do you trust them to be home alone?  I bet you're scared, huh?", 'I am nervous, but I am going to give it a try. I am pretty confident in their abilities for handling emergencies.']
That's good.  You're a good parent!  Good luck with everything!
I have decided to let my kids stay home alone without a babysitter while I work. They have been begging me for this but I have not been confident in their abilities to manage themselves and the house.