Is my phone using both WiFi and 4G? My Samsung Galaxy S4 (Verizon) running 4.2.2 (with the VRUAME7 Build, so root is not an option currently) has both the WiFi and 4G/mobile data symbols in the notification bar, occasionally the mobile data symbol will go away, but it is there more often then not. 



So I have read through this forum and it says that by turning off the Caller Name ID app that this should remove the mobile data from the notifications. I have done this and it has not removed the symbol. 

Questions

My phone does not seem to be using the mobile data, but I would like to know if it is in fact using the mobile data while connected to WiFi?

Shouldn't/Does the mobile data turn off when connected to WiFi? 

If it does not turn off the mobile data, why not and can I fix this with Tasker? That is a HUGE waste of battery!
Your phone is not using both WiFi and 4G, but the 4G radio stays on and stays in sync with the tower (if you move from a 4G to 3G area while still on WiFi, you'll see the icon change when it recognizes the tower swtich).

On my Droid Bionic (Verizon), I have a Tasker script that turns off Mobile Data when I'm connected to Work or home WiFi networks; my battery life is greatly extended with this setup, and the phone works as I expect (I'm told that MMS messages require the Mobile Data connection, but I rarely receive them, so I can't say if that's true; if so, it may be one reason the radio stays on by default).