Remember, when it came to statistical inferences, we made a point to say, "It's not perfect." We saw that with confidence intervals. We ended up seeing that there would be a certain amount of error. And so, while we had confidence in the interval, we also had error. So, when it comes to hypothesis testing, we need to determine what is this error we want to study? What is this error we want to keep in the back of our mind? And we call that error significance level. It's the probability of making a mistake, significance level - the probability of making a mistake. So, particularly, what is this mistake we are talking about? The mistake we're talking about is rejecting the null when in fact the null is true. That is the mistake that we are wanting to determine the chance of making. Now, as a person who's dyslexic, this statement of "reject the null when the null is in fact true" kind of blows my mind. It doesn't really make sense to me. So, let's bring it back to that example of the court system. Let's go back and remember, what is the null statement? When we are looking at a court situation, again, when we're looking at a court situation, the null is: we are assuming a person is innocent. The null is assuming innocence. And so, when we say "when in fact the null is true", we are emphasizing the fact that a person is actually fully innocent. The person is actually innocent, again emphasizing the null is actually true. So, what is rejecting the null mean? Well, rejecting the null means I am rejecting that assumption of innocence. Rejecting innocence means that you are convicting the person as guilty. And should you guys give me a hand here, is it a good thing or is it a bad thing to convict as guilty an innocent person? Oh my gosh, it's terrible. It's literally the worst mistake that you can make when it comes to the judicial system. The absolute most heinous mistake a court system can do is take someone who is innocent and convict them as guilty. That's the worst thing you can do. And so, significance level is then the probability of making this mistake. The significance level is the probability of making the absolute worst mistake. And so, if significance level is representing the probability of making the worst possible mistake, we want to make sure that probability is as small as possible because we want to make sure the probability of making a mistake is so small. So, what does small mean? Well, generally 5%. 5% is what we will use as a significance level. A 5% chance of making a mistake. And that's going to be also the percentage we use if we are not given the significance level but you're allowed to change the significance level particularly if we are in a situation, a courtroom situation, of a person on death row which has very bad repercussions, literally if you convict them as guilty you're gonna kill them. That is a terrible repercussion. Well then, we want that significance level to be even smaller versus the significance level can get bigger when the mistake is less consequential. But the point is these are all still relatively small percentages. And so, let's talk about how we will interpret these significance levels. If you guys look at example one and two here, you'll notice it says "Part two" and it's because I'm actually going to keep referring to these same two examples, the success rate and parents examples, so that we can see contextually how all of these ideas are going to flow nicely together. So, we're still looking at the same statewide success rate comparative to the West Valley success rate. But in particular, we chose a 5% significance level and I want to be able to interpret this. So, the first thing I want to emphasize is I'm using the word "chance". We are looking at a 5% because we're looking at 0.05. There is a 5% chance. Why am I using the word chance? Well again, it's because of the fact that significance level is a probability, alright? So, we start our interpretations of significance level by emphasizing that this alpha equals 0.05. We use Alpha to signify significance level. This Alpha of 0.05 is saying that there is a 5% chance - 5% chance of what? That West Valley will conclude their math success rate in math is higher than the statewide success rate. What this is emphasizing is that we are concluding that our alternative hypothesis as true - the significance level is a probability that we will conclude that the alternative hypothesis is true when in fact there is no difference. Well, remember, no difference means equal. It means equal. So, when in fact West Valley success rate is exactly equal to the success rate of all California Community College. What I want you guys to see here is that being able to write your alternative hypothesis in words is how you will practically interpret the significance level because you are emphasizing what was the alternative hypothesis when in fact there was no difference. Let's try one more. Let's try the parent example - the parenting example about parents who feel their kids are not being taught enough Math and Science today versus in 1994. And we chose a slightly larger significance level, Alpha equals 0.10, where again that significance level, that 0.10, is emphasizing a 10% chance, representing a probability. It's representing the probability we will conclude that the percent of parents in high school whose kids are in high school who feel their kids are not being taught enough Math and Science today is different than in 1994. That entire first bunch of green highlights is emphasizing we are concluding the alternative hypothesis not equal to the alternative hypothesis is going to be concluded as true when in fact there is no difference. I want you guys to notice that the significance level statements always end with when in fact there is no difference because in every situation remember no difference is emphasizing that equality, that equality we already acknowledged in the null hypothesis. I end up writing out in essence the significance level interpretation for you but I did want to emphasize that on the next page I did provide a template, a template for interpreting the significance level listing that percent chance that's your significance level and then in words writing the conclusion of what is your alternative hypothesis and again like I mentioned earlier the statement will always end with when in fact there's no difference because ultimately that's the idea of significance level the actual truthfulness is that there is no difference.