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?