 Hi, this is Dr. Don. I have a problem out of Chapter 2 about a competence interval for a population mean. We're given some data, 12 scores for high school seniors on a test, and we're told that the population is assumed to be normally distributed. And we want to they ask us for the sample mean standard deviation, but their old thrust to the problem is to construct a 95% percent of the population mean. Well, you need to make a decision. Do you do a Z test or a T test? Z distribution or T distribution, I should say. The thing to look for when you're looking at these types of problems, are you given the population standard deviation sigma? If you're not given sigma, then for all of our problems, that means you use the T distribution. And here, we're not given sigma, so we use the T distribution. Let's do this first using stat crunch. And I'm going to go over here and click on our little rectangle, and I'm going to open this into stat crunch. So here's our data. We need the sample mean and sample standard deviation. And the way to get that quickly is to go to stat, where we go for most things. This time we want summary statistics, our data is in a column. I'm going to select the column, and I want the mean and standard deviation. I just hold the control key down to select those and click compute. And there we've got our mean 909.83, around the 0.8, standard deviation 304.7. That's pretty quick. Now, we'll go back to get the confidence interval. We go to stat, and we decided we're going to use T distribution, and we've got one sample with data this time. So, we need to select that column, and we want the confidence interval, and it's a 95% confidence interval, so that's the default. And we click compute, and there we have our answer. And let me move this around a bit, so you can see that our answer is what they want, 716.2, around the one decimal place, 1103.4, around the one decimal place. So that's the stat crunch. Now let's do it using Excel. Click on our rectangle again. We're going to open in Excel. It drops down to the bottom, our spreadsheet with the data. Data comes up. We have to click enable editing. So there's our data. And we can do this very quickly using the data analysis, descriptive statistics tool. And here we get this dialog box. Our data is in this first column, and we need to select that. Let me just select it again to make sure I have the right one. Here we go. Got all the data in there. It's in the column. We don't have labels, so that's unchecked. Output range. I'm going to select, yeah, I think I will select C1. We want the summary statistics. We want the confidence level for the mean, and we want 95% confidence level. And we click OK. And it gets answers, and I'm going to expand as you can see. There's our mean, 909.83, our standard deviation, 304.7. And we've got its label, confidence level, but that's really the margin of error for 95% confidence level. So to get our lower limit, it's just equal the mean minus that confidence. And the upper is equal to the mean plus that confidence. So there's our lower level, 716.2, and our upper level, 11.03.4. So that's quick. And you can do it much faster if you don't have to tell people what you're doing. So I hope this helps.