 Hello. This is a video on how to calculate the margin of error or error bound when developing a confidence interval to predict a population mean. In a survey, 18 people were asked how much they spent on their child's last birthday gift. The results were roughly bell shaped with a mean of $35 in standard deviation of $6. Find the margin of error at a 90% confidence level. Give your answer to three decimal places. So first thing I want to do is I need to find my critical value and keep in mind that we are using the t distribution. So use t distribution since you don't know anything about the population standard deviation. Sure, you have a sample standard deviation of $6, but that doesn't tell you anything about the population standard deviation. So we have to use the t distribution. So let's find t sub alpha over two. In this case, our alpha is one minus or confidence level. That's one minus point 90. That is point one, which means alpha over two or point one divided by two is going to be point zero five. So that means I'm looking for the data value whose area to the right is point zero five. So area to the right is point zero five. When I go to find this critical value, I need to know the area to the left. So one minus point zero five, which is point 95 in this case. One other thing I need is degrees of freedom. The only thing you need to know about t distribution is its number of data values from sample size minus one. 18 minus one is 17. And what this is going to give me is this is going to give me my critical value t sub alpha over two. So let's go to Google Sheets and let's figure this out. So when you get to Google Sheets, you will go to the compute tab. You will go to the t distribution region. Degrees of freedom is actually 17. And the only other thing you need to type in is the left tail area. The left tail area in this case is point 95. This gives me a critical value of about 1.74. Anytime you're trying to find a data value from an area with the t distribution, there's no need to mess with mu and sigma up here. So 1.74 is what we are going to use. 1.74. Well, other stuff we need for a formula. We need our sample standard deviation S, which would be six. Then we need our sample size N, which is 18. Plug this into the error bound formula. And you have 1.74 times six divided by the square root of 18. So I recommend doing six divided by the square root of 18 first. Keep it in your calculator and multiply by 1.74. When you do this, you will obtain an error bound or margin of error of 2.461. 2.461. And that's how you calculate the error bound when making a confidence interval for a population mean.