 Hi, this is Dr. Don. I've had some questions about how to find confidence intervals using Excel, and I'll show you how to do it using basic Excel functions first, and then we'll look at how to do it using PHStat. I've set up my spreadsheet here. I've got some data in column B. The alpha we're given is 0.05, which is a 95% confidence C. And in order to find the confidence interval, we need the mean and the standard deviation, and then the count. I'm going to click in this cell here by the mean, average, they don't have a mean in Excel, and we just need our range. We don't want to include the, well actually it won't matter because it doesn't count a non-numeric. That gives us our average, and I've got a formula over here in these NA cells that will show you the actual function, the equation we're using. Standard deviation equal, start typing ST standard, woop, STD, and we look down there and we've got standard deviation P, which stands for population and dot S, which stands for sample. This is a sample, so I want to select that one, and I just highlight my number again, my column, make sure I get them all, hit enter. I've got my standard deviation, and then finally is the count. You might guess we use the count function, and again we've got our range there, and hit enter. So now we've got our basic there, our average salary for these people at 60, roughly 66,000 with a pretty wide range there. We've got some 152, 47, so the standard deviation is huge in this sample. If we know the population standard deviation, we can use the Z distribution, or sometimes if you have an N greater than 30, which we do here, you can use the Z distribution as well, and let the standard deviation of the sample approximate the standard deviation of the population, which it may or may not, depending upon how good your sample is. So we're going to get our margin of error, we're going to put our cursor there, equal, start typing confidence. We've got confidence norm and console.t, we want norm, which has the Z distribution. We need alpha, comma, our standard deviation, make sure we get the right cell, that cell, comma, and then our size, which is our count, and then close it out and hit enter. So that's our margin of error for the normal distribution. The lower limit is just equal the mean plus, excuse me, minus the margin of error, enter, and the upper limit is equal to the mean plus the margin of error and hit enter. Okay. If we know the population standard deviation, which you should most of the time, if you're using the normal, you would just enter it there instead of using the sample standard deviation as we have here. To get the distribution, it's very similar, equal, confidence, get the confidence t, alpha again, comma, standard deviation, comma, size, close it out. And we've got a very similar margin of error, equal mean minus equal mean plus. And they're very similar, which we'd expect. As the n gets large, the z and the t distribution start to converge. You can see they're pretty close there. And again, we would normally use the z distribution if we know the standard deviation. Okay, let's do it using pH stat. And the way we do that, it will either be in your add-ins that you'll get pH stat, or it depends on how you install it, you'll have pH stat as a tap on a sign. We look and we find confidence intervals. And the first one, estimate for the mean sigma known. So we're gonna click on that one to get the normal distribution. Our population standard deviation, see, get asked for that. We've got to input that. I'm just gonna say, let's say that the population standard deviation is only $24,000. We've got 95%, which is the same as .05 for alpha. And instead of using the sample size and the mean, I'm gonna click on sample statistics unknown, and then we're gonna click in that box, highlight our range of data again. It is assuming that you don't know. Down at the bottom, you've got an option for finite population. If you think your sample size is more than about 5% of the whole population, you need to double check that. Here, we know our population of employees is gonna be several thousand. So a sample of 30 is nowhere near 5%. So we can ignore that for now. And I'm gonna click okay, and it inserts a table here, and it gives us, there's where I put in the population standard deviation, and the sample means you have the same size to count confidence, and it gives us a range of 58,000 to 73,000. And again, this is the Z distribution. You can see that as opposed to the 55 to 76. To get the T distribution, we do something similar. We go back to confidence, whoops, you need to be on the page with the data, confidence, interval, sigma unknown, which gives you the T. Again, I'm gonna assume we don't know those. Click in there, and I'm going to select the same data range again. And again, we don't need to finite. I'm just gonna click okay, and we get another tab inserted that gives us the same information. This is identical to the T that we got here, 76, 634, 555, 76, 34, 555. So that's how you do it using the PH step add-in. So I hope this helps.