Yes, Simple Google Anlaytics fixes it all for you.
The first thing you have to do is completely REMOVE any trace of code you personally pasted into your site. Then install my Simple Google Analytics mod (follow the readme, it's pretty straight forward).
If using Zen 1.5 you'll need to register the page in the admin (if not, no worries).
Then from the admin configuration just enter your Analytics tracking id (and Adwords conversion tracking if you are using that).
Save and you're all set.
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