there are typos in your example code
The post example under step 2 provided on the page https://developer.bose.com/soundtouch-control-api/apis contains typos and thus doesn't work.
on line 3:
var data = "PRESET_" + presetNumber + "</key">; --> " and > need to switch places
in the alert:
alert('Status: ' + jqXHR.status = ' ' + jqXHR.statusText + '.' + 'Response: ' + jqXHR.responseText); --> the = following jqXHR.status needs to be between quotes and you should add another +