 Hi, this is Dr. Don. I have a problem at a chapter six about a confidence interval. And if we read the problem, it says a publisher wants to estimate the mean time. So that's something about the population mean because it says of all adults reading newspapers. He takes a sample of 15 people, which is a small sample. And from past studies, the publisher assumes this is the Greek letter sigma for the population standard deviation, which is important, is 2.1 minutes and that the population of times is normally distributed. Okay, this is a small sample and you would think about using the t distribution, but here we know the population standard deviation sigma. And so in our course, whenever you know sigma, you use the z distribution. We're going to do this using stat crunch. You're going to click on the little blue rectangle to load this raw data instead of keying it in and then open in stat crunch. Okay, we're over here in stat crunch. We have our data in this column labeled variable one and we want to run a z test. Now we had one sample. So we clicked on stat and we look for z for z distribution, one sample, and then we have data this time. We don't have the summary. We have the data. So I'm going to click on that, open up the dialog box. I'm going to select the column that has our data in it, variable one. And here's a critical point that many people miss. We have the sigma. So we need to enter that 2.1 minutes. And we want a confidence interval note. We could run a hypothesis test with the same setup. But here we want the confidence interval and we want 0.90 for 90%. And I'm just going to click compute. And we get our answer here, 90% confidence interval for the mean. There's the sample mean 8.6. There's the standard error, which we don't have to calculate. Stat crunch does it for us. And a lower limit of 7.7 upper limit of 9.49. Now they say round to one decimal. So that would be 7.7 and 9.5. We look over here in stat crunch and it says 7.6 and 9.6. But on this problem, it gives us a limit and an allowance of plus or minus 0.1 to allow for different types of technology. So that would be the right answer. The second part of the question says, what is the 99% confidence interval? And all we have to do in stat crunch is just to click on options, click on edit. And then we go back here and just change our confidence interval to 0.99 for 99%. Click compute again and stat crunch updates. And now we've got 0.54 still for the standard error. That doesn't change. But our lower limit is 7.2 rounding to 1 tenth. And the upper limit rounds to 10.0. And now if we look over here, we have the right answer there. And the final part is, which interval is wider? Well, it's calico basketball hoop. The wider the hoop, the more confident you can be. So here the 99% interval is wider. And you can see that it goes from 7.2 to 10, which is wider than 7.6 to 9.6. Hope this helps. And if it does help, please consider subscribing to my YouTube channel, The Stats Files. Just click the big red subscribe button.