document.getElementByID is not a function

It's document.getElementById() and not document.getElementByID(). Check the casing for Id.

In my case, I was using it on an element instead of document, and according to MDN:

Unlike some other element-lookup methods such as Document.querySelector() and Document.querySelectorAll(), getElementById() is only available as a method of the global document object, and not available as a method on all element objects in the DOM. Because ID values must be unique throughout the entire document, there is no need for "local" versions of the function.

It's getElementById()

Note the lower-case d in Id.

I've modified your script to work with jQuery, if you wish to do so.

$(document).ready(function(){
    //To add a task when the user hits the return key
    $('#task-text').keydown(function(evt){
          if(evt.keyCode == 13)
          {
             add_task($(this), evt);
          }
    });
    //To add a task when the user clicks on the submit button
    $("#add-task").click(function(evt){
        add_task($("#task-text"),evt);
    });
});

function add_task(textBox, evt){
  evt.preventDefault();
  var taskText = textBox.val();
  $("<li />").text(taskText).appendTo("#tasks");
  textBox.val("");
};