Checking whether a string is capitalized or not (python)

thanks in advance for possibly helping me to solve the following problem...

It's my aim to separate strings from a list into two categories (upper- and lowercased) and give feedback wether an item is capitalized or not. Here is what I tried so far:

names = ["justin", "Noah"]

def check_upper(strings):
    i = 0
    uppercased_strings = []
    lowercased_strings = []
    for string in strings:
        if string[i].isupper() == True:
            print("String is uppercased!")
            uppercased_strings.append(string[i])
            i += 1
        elif string[i] != True:
            print("String is lowercased")
            lowercased_strings.append(string[i])
            i += 1
        print(uppercased_strings, lowercased_strings)

check_upper(names)

But sad enough I get this output when running the script:

String is lowercased
[] ['j']
String is lowercased
[] ['j', 'o']