What we're going to do here to just wrap up our discussion about confidence intervals is just do a quick comparison. A quick comparison between confidence level and frankly how much error we can have, alright? So what I'm going to do is I'm gonna actually have us go back to our Arnold Schwarzenegger example. So let's just scroll back really quick, let's go back to our Arnold Schwarzenegger example, and let's remember we actually found a confidence interval. A confidence interval that had a 95% confidence level, alright? And so what I want us to do is I practically want us to just look at this confidence interval. Alright, looking at this confidence interval, it went from a value as low as 0.546 to a value of 0.584. And practically what this lower and upper value is, is that again it's representing the width of my confidence interval. Again, this lower and upper value is representing the distance in which my percentages can be. And so ultimately what is then the width of my confidence interval? It's then that distance from the lower to the upper value. So how can I find the width? I can then subtract the upper value minus the lower value. I can subtract the upper value minus the lower value. So we can see here that this 95% confidence level has a width of 0.038. And what I want us to remember is that when it came to these confidence intervals, we had the sample proportion be in the middle. We had the sample proportion in the middle, and we then either added or subtracted a margin of error to get to that upper and lower value. And so what I want you to see here is the width is equal to two margins of error. Or dividing both sides by two, we can ultimately see margin of error is then half of the width. We then can see margin of error is then half of the width we just found on the previous column. So dividing 0.038 by two we get 0.019 or as a percentage we get 1.9%. Interesting when I created a confidence interval with a confidence level of 95%, I had 1.9% error. If we were to go back to our Arnold Schwarzenegger example and keep everything the same but my confidence level changed, my confidence level went to 80%, the confidence interval would end up being 0.553 to 0.577. So if everything else remained the same, the only thing that changed was the confidence level. I want you to note the confidence interval changed and what I want you guys to do is really quickly find the width of this new interval and more importantly find the margin of error of this interval. Why am I having us do this little exercise? Ultimately I like to use color and the two main ideas are green and orange: error and confidence. Whenever it comes to doing any type of statistical study, these are always the two big things researchers want to keep in mind: how confident do I want to be and how much error am I willing to have? And so say you're going fishing, right? Say you're going fishing and you're going fishing the old school way, you're going fishing using a net. Ultimately, your confidence that you will get a fish will go up when the size of your net is bigger. Ultimately, you will have more confidence if you have a bigger net, if you have a bigger interval. Why? Because you're more likely to catch things. The bigger the net, the bigger the interval. So that's a good thing, right? Good thing. Good thing is having lots of confidence. It's good to have an increase of confidence. But what I want you to then see on the other side of the table is that if your confidence goes up, notice how your error also goes up. And we know in general in life, we don't want more error, we want less error. And this brings us into a pickle because notice as we get one good thing, right, meaning if I get more confidence, I get one thing wrong, dang it, I get more error. And so if I wanted to then decrease my error, man, my confidence goes down. And so the big question is, how can I have both? How can I have both? How can I have both high confidence but low error? Because that's really what we want in life. We want to be highly confident with as little mistakes as possible. How do I get both? And that, guys, is where we get into the next section.