How to handle exceptions when writing javascript library methods

Question

I am writing a JavaScript utility for myself as a learning experience, and my question is. When I need to throw an exception in my code when testing an argument or use something, should I use throw new TypeError();or throw TypeError();, or should I not check at all and just let it work with an error? I'm not sure if this is important. Of course, I understand the dynamics of exception handling, but is it better for me to deal with these exceptional cases as a lib writer or to let the user test them? For example, if I or someone using my library calls a method from the library with the wrong type of argument, which I should choose, if any.

var Lib = {
    method1: function( /* bool */ do_task ) {
        do_task = do_task || false;
        if ( typeof do_task !== "boolean" ) {
            throw new TypeError( "argument[0] should be true or false" );
        } else {
            if ( do_task === true ) {
                // perform some operation.
            } else {
                // perform some other operation.
            }
        }
    }
};

- , , . . , . ? ?