This is a question from April 2018 QAS, Calculator Section, Problem 29.

I can’t figure out why choice D is the correct answer. I was stuck bw choice A and B, and picked A. Why is A wrong and D correct?

Thank you!

Choice A is wrong because it states with certainty that all prairie dogs in the population are within that weight range. You can never know from a sample, especially a small one, that there are no outliers in the population. (No matter how careful you are in sampling, you never REALLY know about the whole population unless you study the whole population.)

Choice B is wrong because there can and should be individual weights far from the mean–what about the baby prairie dogs? They can’t possibly weigh almost as much as the adults, can they? And what about the very big ones? If there are tons of very big ones and tons of babies, maybe they cancel each other out without impacting the mean much, but that would mean there are lots of prairie dogs outside of that range.

What the margin of error actually tells you is how likely it is that the sample you’re looking at is representative of the total population.

In this case, that means that even though the 30 prairie dogs sampled had a mean weight of 0.94 kg, the actual mean weight of all the prairie dogs in the colony (i.e., the populatoin) is probably 0.94 kg plus or minus the 0.12 kg margin of error. Choice D basically says that.