 Hello. This is a video on using the t distribution versus the z distribution or standard normal distribution when trying to find critical values. You intend to estimate a population mean with a confidence interval. The population standard deviation is unknown. You believe the population to have a normal distribution. Your sample size is 18. Find the positive critical value that corresponds to a confidence level of 99.9%. Most commonly, we've used the standard normal distribution to calculate critical values. However, a general rule to understand is that anytime the population standard deviation, which remember that sigma is not known, we have to use something called the t distribution. And the bigger the sample size is, the more the t distribution actually approximates the standard normal distribution to pretty much come to be the same exact values. But it's important to know population standard deviation sigma when it's not known, you have to use the t distribution. So we're still going to find alpha over two, except now we're looking for t sub alpha over two. That's what we're looking for. Well, who is alpha? Alpha is one minus the confidence level one minus 0.999. That would be 0.001 alpha over two. That's 0.001 divided by two. That's 0.005. So in my data that is approximately normally distributed, I'm looking for the data value is area to the rise point 0.0005. So 0.0005. Well, to use Google Sheets in a minute, I have to know the area to the left. So one minus 0.005 is going to give me 0.9995. All right. So and one other thing you need in order to do the t distribution in Google Sheets or any form of technology is the degrees of freedom. Now, it's really not that important that you understand all the theoretical concepts behind degrees of freedom. But the degrees of freedom is always in minus one for the t distribution. So 18 minus one, that gives you 17. So let's go to Google Sheets. And Google Sheets, you will go to the compute tab. You will go to the t distribution area. And the only thing you have to put in is degrees of freedom, which is indeed 17 in this case. And then you're going to put in your area to the left, which is 0.9995. And as you can see here, our critical value is going to be about 3.97. So 3.97 is what we're going to use for our data value for a critical value 3.97. So the answer is 3.97. That is our critical value. Remember, we had to use the t distribution here because the population standard deviation was not known. And that's always going to be the case. Thanks for watching.