Apnea of prematurity occurs when premature babies have shallow breathing or stop breathing for more than 20 seconds. Researchers assigned a treatment group to receive caffeine therapy and a control group to receive a placebo. Of the 937 random infants given therapy, 377 suffered from death or disability. The placebo group had 932 random infants, and of these, 431 suffered from death and disability. So, the question is: Does caffeine therapy lower the rate of death and disability? As a researcher, what you're interested in is, did the child die from death and disability, and you're hoping this caffeine therapy you are developing will bring down the rate in which children will die. There are pretty clearly two different groups here; they're literally told as the treatment group and the control group. Ultimately, it's these babies, it's these infants that are receiving caffeine therapy and the control group who's receiving the placebo. So, we can write down these two groups. Group one are the infants who are receiving caffeine therapy, and group two are the infants who are receiving placebo. Here's the funny thing: Identifying these two groups, that's actually stuff we did back in Chapter One when we studied observational versus controlled experiments. We identified our treatment and control group. Let's just apply that skill again. And remember when it came to comparing two groups, this was always what I called Step Zero: You got to write down who are your two groups you're even studying. So, this skill of identifying the two groups is ultimately a skill that we learned both back in Section 1.5 as well as in Section 7.5. And so ultimately, I want you to see that right off the bat, we are looking at two groups. So, what do we need then to know? I can use this exact template for my hypothesis test. Well, for starters, we need to even make sure this is going to be a hypothesis testing question. And remember, hypothesis testing questions were all about comparing, was all about forming an inequality comparing to two different values. So, notice that we already have that here. We can know that we're running a hypothesis test because we are being asked to do a comparison, literally in the form of the word "lower" and a comparison of two populations. We already identified those two populations: Infants receiving caffeine therapy and infants receiving the placebo. So, I want you to know where we're already partway there. We already know that we're doing a hypothesis test; we already know we're looking at two populations. And they're running a hypotheses tests because we're being asked to do a comparison, literally the word "lower" is emphasizing a comparison. So, the big question is: Why do I use the letters P? Well, again, we use the letter P when we know my variable is a categorical variable. So, really what this requires is for you to look at the study and the study's success. Are those who suffered from death and disability? I know that seems weird to call that success, but it's simply just asking what is the variable: did they or did they not suffer? Yes or no? And because this is a categorical variable, that is the reason why we know, okay, we are going to write a hypothesis testing using proportions. And so, what I'm trying to help you guys do visually is be able to pull from the prompt those key ideas that will let us know we really have the three check marks in this problem. It's a hypothesis test of two population proportions. And if that is the case, then the template hypothesis is then always going to be that the null is P1 equals P2, and the alternative is then P1 is related somehow to P2. And that we literally identify that inequality from that comparison word "lower," from that comparison word "lower." And why don't you guys give me a hand here: the word "lower," which inequality do you think that is going to dictate for us? Yeah, it's going to be the less than symbol. And that's it. Literally, if you really zoom in on the hypothesis, it's really that easy. It's literally just identifying the inequality as long as you acknowledge that we're looking at two populations, the P1 and P2 and proportions, the fact we're even using the letter P.