 Hey, Jim. This is Don. This is just a quickie to show you how to solve this problem in stat crunch Those equations always kind of look kind of complex, but the easy way to do it. We're going to open it in stat crunch Okay, we have the data there of the four 13 patients Sleep before sleep after using the grug. We're just going to real quickly. We're going to go to t stats paired sample I'm going to select column one sleep before sleep with the drug I want to say the difference is going to show you a trick in a second We want the confidence interval this time and it's just point nine. I Think that's what they wanted was the 90% right just click compute and There we get the answer the lower limit minus 1.99 our planet minus 1.38. Let's see Yeah, that's the answers they have there the other thing I wanted to To show you you remember in some problems. We're given the we're asked for the intermediate values, which are hard to get and in stat crunch sometimes, but if you need the the D bar are the S of D D bar remember is just the mean of the differences and that's the reason when I Did this I clicked on save the differences And that developed that Column there so the D bar is just the mean of those values S of D is the standard deviation of those values and we can get those Pretty quickly by going to summary stats column and I'm going to select the differences I'm going to hold down the control key and select mean and Standard deviation. Whoops. Let's take them off. There go mean Standard deviation click compute and there's my D bar right there the mean of these differences and the S of D the standard deviation of those differences So I hope that helps