A pain relieving medicine claims to contain 500 milligrams of
pain-relieving acetominophen per pill. You measure the mass of 600
milligrams. What can you conclude about the pill?  Is there
pharmaceutical company being honest?

The pill contains materials other than acetominophen .The most common
is binding material.This is used to bind the pills components into a
uniform ,easily taken shape. Some common binders are povidone, xanthan
gum and Carbopol.

Other things that may be present are disintegrants to help the
break-up of the pill in the stomach and coatings help to prevent the
pill from dissolving too soon.

So just to finish up, yes, it contains 500 mg acetominophen and 100 mg excipients.

To correctly answer that question you would need more information.  Of
course there are other substances in the pill, but you only know the
total mass of the pill and not just the mass of the other consituents.
So the mass of the other constituents could be 100g, in which case hte
pharmacuetical company is being honest.  But the mass of these
constituents could be more than 100g, which would mean that the mass
of acetominophen would be less than 500g.
Quiet simply, unless you know the mass of the other constituents, or
do a detailed analytical chemical study of the pill, there is no way
of telling what the exact mass of acetominophen in the pill is.

Damn, if you'da given us the mean and standard deviation of a testing
group, we coulda gone crazy figuring out P-values, and alpha values,
truly find out if the company is lying, or if the data is
statistically insignificant!!! haha [/end me being a nerd]