Outgoing calls that I'm not making

I discovered today that my phone makes an outgoing call to the same number everyday at the same time.  I'm a bit scared as I have other mysterious (stalker) things going on online.  So I contacted tech support at Comcast.  They weren't sure what phone number I was referring too, even though I only have one landline.  They told me to call the manufacturer of my phone as they couldn't see the outgoing calls.  So not sure if I was really even chatting with tech support.  Then I called in (was a bit scared too since I know my phone has been hijacked) and asked them for a new phone number.  A new number has shown up on my account but does not work, and my old one is still there.  I'm scared to call again in case my call is rerouted - Comcast asks for so much personal information to verify your account that I'm getting nervous.  I know this is becoming very common and I'm surprised that Comcast seems to have no solution.