 Today, we're going to talk about confidence intervals, how to find critical values. For a confidence level of 95%, find the critical value around the two decimal places. A critical value is of the form z sub alpha over 2. It means let's find the z score or data value whose area to the right is alpha over 2. So if I have my bell curve, you can see that I have the bell shape and I have this region to the right with area alpha over 2. I want to find the data value whose area to the right is alpha over 2. So let's start off by finding out what is alpha. Alpha is 1 minus the confidence level. In this case, the confidence level is 95% or better put as 0.95. That is 0.05. Next, we need to find alpha over 2. So take this previous result, we obtained 0.05 and divide by 2. We get 0.025. So that means in my bell curve, I want to find the data value whose area to the right is 0.025. So I'm going to draw a line here. The area of my region is 0.025. And yeah, my region probably should be a little bit smaller than that. But as long as you know the area to the right is 0.025, you're good. All right, well, whenever I try to find out what this critical value or this data value is, I need to know the area to the left. Well, if area to the right is 0.025, area to the left is 1 minus 0.025. So 0.975. So I'll now go to my Google Sheets document. And since I'm dealing with Z scores, data values that are standardized, I know that my mean is 0 and my standard deviation is 1. And I also know that my area to the left is 0.975. So let's go to Google Sheets. You're going to go to the Compute tab. Then you are going to go to the Normal region. The mean is 0. Standard deviation is 1. And the only other information you need to put is the left tail area, 0.975. And this actually gives me an answer of about 1.96. 1.96. So my critical value in this case, Z sub alpha over 2, is 1.96. And this is actually a common critical value that's used in statistics. 95% confidence levels are actually very popular. So 1.96 is our answer. Thanks for watching.