Your code is working. Since the letter 'B' comes before the letter 'a' in Unicode, it follows that "Banana" comes before "apple". Have a look at this overly complicated article: Latin script in Unicode and you'll see that 'B' is represented by 66 and 'a' is represented by 97.
But you don't care whether it's "Banana" or "banana", right? You don't care about upper and lower case. So I'd suggest using the toLowerCase() method of String and compare the lower-case versions of the two strings.
Check lines 4 and 7. Are you sure those statements are actually changing any values that the rest of your program is using? Remember, strings are immutable. That is, you can't change a String; you can only get new Strings.