When it comes to our calculator work, we go "Stat", "Test", 1-PropZTest, and we plug in the P_0, the X, the n, and the inequality that we use in alternative hypothesis. What P-value did you get when you type into 1-PropZTest my status quo of 11%, success amount of 43, sample size of 500, and choosing the less than symbol? Yeah, we'll ultimately get 0.04 for my P-value. My Z-test statistic will be 1.72. My P-value is 0.04. So, we found the P-value. And remember, the decision step is ultimately going to take the P-value from step three, the significance level from step two, and compare them. Compare the P-value of 0.04 to the significance level of 0.05. And again, when it comes to comparing these two values, it's always with respect to the P-value. Is the P-value bigger or smaller? Which one do we have here when comparing the P-value? Is it bigger or smaller? It's smaller. And so, what is the result? When your P-value is smaller, you will reject the null. Why? Well, let's go back a couple pages. Remember that the idea of P-value and significance level is from the point of view of the jury. And when your P-value is small, it means that your sample was so extreme. Your P-value is small because your P-value is so extreme. You're looking at just this tail on the normal curve. And remember, when your P-value is small, it means that your sample is weird. So weird that it is surprising. And remember, as a jury member, if you're hearing a testimony, hearing a report that is surprising, if you're hearing something that's surprising, that is usually the evidence a jury member needs to reject a person's innocence, to convict a person. And so, that's the relationship here, is that when P is smaller, we reject the null. And there is significant evidence. So, going back to my example, ultimately, the smaller the P-value, we reject the null, emphasizing there is enough evidence. And it's these three ideas that will also and always go together: When your P-value is smaller, you reject the null, and there is enough evidence. These three will always go together when it comes to hypothesis testing. Since P-value is smaller, we reject the null, and therefore, there is enough evidence showing what I wanted to find in my alternative hypothesis. And again, my alternative hypothesis is simply the question: Does the data show that the proportion of Americans with Myspace accounts has decreased since 2009? We take that question in green and you regurgitate it to answer it as a sentence: There is enough evidence showing, knowing that the proportion of Americans with Myspace accounts has decreased since 2009. I'm literally answering the question. I literally answered the question: There is enough evidence showing the proportion of Americans with Myspace accounts has decreased since 2009. Notice we use the exact same outline, exact same structure to run both hypothesis testing problems. Notice that almost steps one and two were simply just identifying the key numbers in blue and in green and in purple and in orange so we knew how to plug them into the calculator. And then, ultimately, step four is either getting one of two results: either P is smaller or P is bigger. And that based off of if P is smaller or bigger, you then have a domino effect of results: you either fail to reject the null, there's not enough evidence, or you reject the null, and there is enough evidence. Great thing about hypothesis testing is it's very, very methodical.