In jQuery:
To check the checkbox:
$("#checkboxid").attr("checked","checked");
To uncheck the checkbox:
$("#checkboxid").removeAttr("checked");
The other answers hint at the solution and point you to documentation that after further digging will get you to this answer. Jukka K. Korpela has the reason this is the correct answer, basically I followed his link and then looked up the jQuery docs to get to that result. Just figured I'd save future people who find this article those extra steps.