 Hello. This is a video on calculating the margin of error or error bound for confidence intervals. In a recent poll, 150 people were asked if they liked dogs. 46% said they did. Find the margin of error of this poll at the 99% confidence level. Give your answer to three decimal places. So my formula for my error bound is actually error bound is equal to your critical value times the square root of p hat times q hat divided by n. Well, first and foremost, I want to go ahead and make a note here that says p hat. This is my sample proportion. In other words, in my sample, the proportion of people, in this case that liked dogs. p hat is 0.46. q hat is one minus p hat. One minus the sample proportion. One minus 0.46, which is 0.54. And then n is my sample size. In this case, my sample size is 150. And we now need to figure out the critical value. This is alpha over two. This is the z score or data value whose area to the right is alpha over two. So I'm going to end up having a bell curve. And I'm going to be looking for some data value with some area to the right. What is alpha over two? Well, first off, alpha is always going to be one minus the confidence level. One minus 0.99 in this case, which is 0.01, which means alpha over two or 0.01 divided by two is going to be 0.005. So I'm looking for the data value whose area to the right is 0.005. Well, that means that to find the data value, I need to know the area of the region to the left, which is one minus 0.005 or 0.995. And I can use Google Sheets to find my critical value. So let's do that. In Google Sheets, to find critical values, go to the compute tab. Go to the normal area. We're dealing with z scores to the mean of zero, standard deviations one. The area to the left or the left tail area in this case is going to be 0.995. Gives me a z score of about, we'll go with 2.576. 2.576. 2.576. And now we have all of the ingredients to calculate our error bound or margin of error. My critical value is 2.576. And underneath the radical, I'm going to have 0.46, which is P hat times 0.54, which is my Q hat, all divided by the sample size, 150. You will want to use a calculator to evaluate this. So I have about 2.576 times underneath the radical. You should get approximately 0.04069. It's probably wise to calculate your radical first. Keep this answer in your calculator and then multiply by 2.576. This is going to give you 0.105. My error bound or margin of error is 0.105. Anytime you have to find the margin of error or the error bound, technology will not find the final answer for you. You have to calculate the error bound or margin of error by hand. The technology will not give it to you once again. Thanks for watching.