One of the things that we know is that 1.96 represents 95% confidence interval when it comes to normal distribution. Data Analysis, Microsoft Excel, Statistical Analysis, Normal Distribution, Very useful for beginners as well as anyone interested in learning some basics. At 50, they're almost identical. This professor does an exceptional job of breaking down complex concepts and calculations without diluting the material. Let’s see how we can find out the confidence interval for a population means based on the sample data provided. We are 95% confident, that the population parameter, the temperature, the average temperature for New York, falls somewhere between these two values. This course is part of the iMBA offered by the University of Illinois, a flexible, fully-accredited online MBA at an incredibly competitive price. 1.97 multiplied by 1.266, so this is my t value and this is my standard error. So I'm going to highlight this for you to remember, you will use this value. This course is part of the iMBA offered by the University of Illinois, a flexible, fully-accredited online MBA at an incredibly competitive price. And you want to remember that, that it's 1.96. So first I'm going to show you the z value, then I'm going to show you the t value. So again, let me go back to my simulation so you can see that visually. But in the PowerPoints I've been telling you that if your sample size is large enough, we can use a Z-distribution, because as the sample size gets larger and larger the t distribution. And if I say I'm looking for a confidence interval of 95%, I am saying that here it's 95%. To be exactly right, we should be using a t-distribution. • Use Excel for statistical analysis. That's why in my slides I have told you when the sample size is large enough, you can go ahead and just use 1.96. It's going to be my standard deviation divided by the square root of my sample size. What you see then as it becomes closer and closer to 50. So in this case, we got a sample that gave us the right answer. So it.s .975 and this is going to be close to 1.96. How to Compute Confidence Interval? So now that I have my margin of error, the lower bound of my confidence interval is going to be my sample mean, so the equation for my confidence interval is X bar + or- margin of error. So, a significance level of 0.05 is equal to a 95% confidence level. =CONFIDENCE(alpha,standard_dev,size) The CONFIDENCE function uses the following arguments: 1. Confidence Interval value is arrived by adding and subtracting the confidence value from the MEAN of the data set. Your critical value, how far you are from the mean in that distribution times your standard error, which is right here. • Summarize large data sets in graphical, tabular, and numerical forms. So the way I find that is by taking its average, and the average of the values that sits right here. For more information, please see the Resource page in this course and onlinemba.illinois.edu. So remember what the confidence interval of 95% will be. Look at the red line versus the black line. The ‘CONFIDENCE’ function is an Excel statistical function that returns the confidence value using the normal distribution. The black curve is the normal distribution. In the Power Points, when we don't have access to t distribution I have said to you that we can go ahead and use a z value. And what was our temperature? This is my mean of my sample- the margin of error. • Understand why normal distribution can be used in so many settings. A 95% or 0.95 confidence interval corresponds to alpha = 1 – 0.95 = 0.05. There is a 5% chance that we would have had something that did not result in this value. Specifically, you will be introduced to statistics and how to summarize data and learn concepts of frequency, normal distribution, statistical studies, sampling, and confidence intervals. If you want to be more definitely you can calculate a 99% confidence interval. So Degrees of Freedom is always n-1. Size (required argument) – This is the sample size. Assume that intelligence quotient (IQ) scores follow a normal distribution with standard deviation 15. Let me just in this video show you a simulation where it shows the difference between a t distribution and a normal distribution. So, if you look at this one you will see that it's the average of where the data for New York sits. I have already gone ahead and calculated my average based on the entire data set that I have. 3. In the spreadsheet below, the Excel Confidence Function is used to calculate the confidence interval with a significance of 0.05 (i.e. That will, again, mean you can be 99% sure that the confidence interval of your sample size contains the population mean. If you look at this animation that's happening right here. That means if i were taking samples over and over again that's what I would get. Exploring and Producing Data for Business Decision Making, University of Illinois at Urbana-Champaign, Managerial Economics and Business Analysis Specialization, Construction Engineering and Management Certificate, Machine Learning for Analytics Certificate, Innovation Management & Entrepreneurship Certificate, Sustainabaility and Development Certificate, Spatial Data Analysis and Visualization Certificate, Master's of Innovation & Entrepreneurship. Confidence Interval = Sample Mean ± Confidence Value. So we have over 26,000 data points for New York for over 25 years of data that we have for average daily temperatures. And then, it's going to be upper value is going to be 56 + the margin of error. The area to the left of this Z is really actually .975. Pick the first value, again control shift down, close the parenthesis, return. So then I want to know what is this z value, and this is what we call z of alpha over 2 And Z of alpha/2. Z would have given me 1.96, using a t distribution I get a 1.97. It's minor problems. © 2020 Coursera Inc. All rights reserved. Standard_dev (required argument) – This is the standard deviation for the data range. So I'm going to click on the first value, hold Ctrl+Shift, and I will pick the entire 200 points. You want to compute a 95% confidence interval for the population mean. supports HTML5 video. So but being accurate and being in excel, I am going to actually use the correct one which is the T distribution. The sample mean is … And the Z-distribution starts to become very similar. Now based on this I need to calculate the standard deviation for this sampling means. So I would press return and this would be the standard error which is the standard deviation of the sampling means. CI = 52 ± 8.30; CI = 52 + 8.30 or 52 – 8.30; CI = 44.10 to 60.70. [MUSIC] In this video, I'm going to show you the concept of confidence intervals. The red line is the four to t distribution and it becomes more and more like a normal distribution as the sample size increases, but look at its tail, it's just longer, slightly longer. One is positive and one is negative. So I will return that and you will see that these numbers are pretty close. This will be accomplished through the use of Excel and data sets from many different disciplines, allowing you to see the use of statistics in very diverse settings. In turn, the confidence value is used to calculate the confidence interval (or CI) of the true mean (or average) of a population. So that's exactly what that equation is. Things to Remember Here. 2. The significance level is equal to 1– confidence level. So let me get rid of this drawing. And how do I know this? Key distribution looks exactly the same here except it's tail is a little longer. Alpha (required argument) – This is the significance level used to compute the confidence level. And that's one of the things that I have said to you, that 95% confidence interval is very common. And you need to scroll up just a tad to see it again. • Use sample information to infer about the population with a certain level of confidence about the accuracy of the estimations. A confidence interval tells you the range of values where the true mean (the average) for a population should fall based on a sample. Confidence intervals are a way to acknowledge the uncertainty in your data in a structured and scientific fashion. And that gives me the average of 55.2, and it gives me the standard deviation of 17.38, roughly. The formula for that is the standard deviation of the sampling means is known as a standard error and we use the sample standard deviation and divided by the square root of n. So this is what I need to do. Clinical Professor of Business Administration, To view this video please enable JavaScript, and consider upgrading to a web browser that. So then what is these two values? And for 95, I pretty much know that's a 1.96. Then the confidence interval. The course will focus not only on explaining these concepts, but also understanding the meaning of the results obtained. • Use Excel for statistical analysis. Default accuracy is usually 95%. So to do that I'm going to say norm.s.inverse and I'm going to put everything to the left of that value.