 This is Dr. Don, and we're going to take a couple of minutes and walk through a paired sample's T-test using statcrunch. Here's the situation. We have a medical researcher that has a new drug and the researcher wants to determine whether or not a drug, the drug, changes body temperature. So they select seven participants randomly chosen and their temperatures are taken before they take the drug and then 20 minutes after they took the drug the temperatures are taken again. Now we're told to assume body temperatures are normally distributed, which they generally are. And we want to use an alpha of point zero five. Our significance level there is point zero five five percent. And we want to know is there enough evidence to conclude the drug changes body temperature? So let's jump into it. I'll show you how to do it with statcrunch. Here's the data on the seven participants. First column is labeled before and it's got their temperatures and degrees Fahrenheit. And then we've got a column label aphrodur. 20 minutes and those are their temperatures. So to do a two sample T-test paired we're going to go to stat first go down to T stats and we want a paired sample not a normal two sample. And we click on that. First thing we need to do is to select the data in column one which is our before data at sample one. Sample two is in the after column. We don't have to worry about grouping or having any special coding here. We do want to save the differences between the two data sets. So that's important. Check that. We're doing the hypothesis test for the mean difference mu d mu one minus mu two. Our assumed null difference is zero. Our alternative is not equal. The researcher wants to know believes that the drug will make a difference in the before and after temperature. We want to get the critical value. So I'm going to click that and double check make sure that the significance level is what we want point zero five down here at the bottom. I want to select the p-value plot just so we can see that plot which can be interesting. And then we click compute and we got our results. First thing I like to do is just read over this top part to make sure it's what I wanted. I wanted the mean difference with mean two subtracted from mean one and our assumption is of not equal for the claim. The difference for after the mean difference is point five five seven and that's one of the answers that you usually have to get. The other thing we need to get is the standard deviation of the differences. This gives us the standard error. And of course we could back that out, but I'll show you another way to get it. Degrees of freedom is in minus seven. We've got our sample sizes seven minus that is six. Our test statistic is one point five nine six. We've got a critical t-value because I checked that and set the significance level is two point four four seven and there's two of them. There's a plus and a minus because it's two tail and we've got a p-value of point one six one six which is much larger than our significance level. If we go here to our p-value plot we can see that these lines are our test statistic above and below because we want to check to make sure it's as extreme or even more extreme and that can be above the mean a positive difference or a negative difference. The area under the curve here is point zero eight above and point zero eight approximately below and that gives us our total of point one six. So that's the first part. Now let's get that standard deviation of the differences. That's why we got this difference column. I'm just going to go over here to stat again and go to summary stats columns and we want the differences and we want to get the mean click on that hold down the control key get standard deviation and then click compute and there's our mean differences the standard deviation of the differences as well. Again you can see the mean here is the same as the mean there and if you did the arithmetic divide this standard deviation of point nine two three five by the square root of seven you'll get that value right there. So I hope this helps.