Using Specifics In Your Sales Copy

I know in copywriting it's always good to include specifics such as... "increase sales by 36%" or "loose weight in 1/2 the time by following this method" or "save up to 2 years of trial and error" or "make up to $4200 per month by following this system" etc. etc.

I'm wondering if these specifics need proof. A lot of the stats that people use in sales letters seem to be specific but really are not, such as "increase sales by 36%" Well, 36% over what? But claims to "make $4200 per month," IMO should be backed up by proof.

Here's a good example of a headline I found in a copywriting course recently where I'm thinking, where do these stats come from? This is an actual headline for a product:

"A Magic Little-Known Piece Of News That Makes A Stock Go Up In Price Within 3-6 Months Of Release - 86% Of The Time"

Now I'm thinking, is there some study somewhere that proofs stocks go up within 3-6 months of release 86% of the time - not 85% or 90%?

I'm wanting to use specific time periods or numbers in my sales copy, but I'm usually hesitant because MY first reaction when reading this is, where do these stats/numbers come from? Are they real? Should I make them up? Should I search for "studies" that have reported stats that I can use to back up my claims?

I know this kind of copy sells, so wondering how to approach it.

Thanks
Tony