Of course, we could not nd the underlying population difference; we had just a sample. But using our sample, we found a difference in sample proportions of pNS − Female − pNS − Male = −0.15. The key question, which we had to defer, was how likely we were to have found a sample difference this large if the underlying population difference were actually zero. This likelihood-this probability-is critical. It is the probability of being wrong if we conclude, based on our sample, that the underlying population difference is not zero. If this probability of being wrong is low enough, we will take the chance. We will conclude that the population difference is not zero and that sex can help explain the choice of a Natural Science major. If this probability of being wrong is not low enough-if a sample difference this large could easily come from a population for which the difference were zero-we will be unwilling to make this leap.