Generally, that’s the idea. For the problem at hand, most likely strata would be levels of employees or job/role, departments, locations, lines of business, etc. with several interviewees chosen at random within each strata. So if done correctly for each company it would be possible that you chose/interviewed same number at each.
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I would have taken the question as assessing the random sample size needed to derive a result representative of the universe.
In the instance at hand, I would have applied the formula (the specifics of which are lost to me in the mist of almost 40 years time), and come up with an answer along the lines of, “To assess Tua Company will require a larger sample size than an assessment of Hurts Company, but nowhere near the 10x proportional difference between the two companies’ headcounts.”
Compliments of Dr. Al Drake’s ST 465 Sampling Methods class, circa 1981.
While the same principles would apply regardless, I would not have gotten into stratifying by qualifications, assuming that the qualified employees of each were equally distributed. If that assumption is invalid, a statistical comparison of the two companies gets really hairy, really fast - which might have been what you intended. And if so, far beyond my capabilities
