Testing if list elements are numerical

I want to define a function with an argument, which is a list:

m = 10;
a = Table[k,{k,1,m}];
TestFun[listArg_] := Sum[listArg[[k]],{k,1,m}]


Now if I run the function,

TestFun[a]


it correctly calculates the sum to be 55.

Now I wish to define the argument of the function in such a way, that it only accepts numerical lists. For single arguments, I know this can be done for instance by:

TestFun[x_?NumericQ] := x


where x is a single number. However for lists, NumericQ returns false. I tried defining the function by

TestFun[list_?MemberQ[#,_?NumericQ]]


but that did not work. Evaluting the function now simply returns:

TestFun[{1,2,3,4,5,6,7,8,9,10}]


I'm on Version 11.

TestFun[listArg_?(VectorQ[#, NumericQ] &)] := Sum[listArg[[k]], {k, 1, m}]

TestFun2[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]


55

or

TestFun2[listArg : {__?NumericQ}] := Sum[listArg[[k]], {k, 1, m}]

TestFun2[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]


55

You can also use the following as the argument of your function:

listArg : {_?NumericQ ..}
listArg_List?(And @@ NumericQ /@ # &)
listArg_List /; (And @@ NumericQ /@ listArg)