How to check a radio button with jQuery?

I try to check a radio button with jQuery. Here's my code:

<form><div id='type'><input type='radio' id='radio_1' name='type' value='1' /><input type='radio' id='radio_2' name='type' value='2' /><input type='radio' id='radio_3' name='type' value='3' /> </div></form>

And the JavaScript:

jQuery("#radio_1").attr('checked', true);

Doesn't work:

jQuery("input[value='1']").attr('checked', true);

Doesn't work:

jQuery('input:radio[name="type"]').filter('[value="1"]').attr('checked', true);

Doesn't work:

Do you have another idea? What am I missing?