 Hi, this is Don, and I want to take just a couple of minutes to show you how to solve a chi-square test for independence using Excel and PhSTAT. It's a little bit different, and so I thought I would show you how to do it. Here's our problem. This is from chapter 10, and it says we've got a contingency table that shows a random sample of adults that rated their local schools and their national schools. And at alpha equal 0.05, can you conclude the adults ratings are related to the type of school? So we want to say, are they independent or are they dependent? So we're going to use StatCrunch. We click on add ends, I'm sorry, PhSTAT, and we're looking for multiple sample tests, and we're doing a chi-square. And it asks us to put in the level of significance, which is 0.05, and then it wants a number of rows, which is two, number of columns, which is four, if I'm counting correctly there, and we clicked OK. And it gives us a table that looks kind of strange here because it's just set up for us to input our data. What PhSTAT does, it will create the basic Excel spreadsheet for you with all the right formulas and linkages based on the number of rows and number of columns. So if I put our data in there, let me go back here to our data. I wonder if I can do this. Control C, and go back here. Control V. Yeah, I pasted the data in. And immediately we've got our answer here. It gives us our expected frequencies. Over here it's showing you, you know, the calculations, and here it gives us the summary, number of rows, number of columns, degrees of freedom, which is the rows and columns minus one, which is larger or in other ways, n minus one times n minus one, which would be one times three is three, I should say it that way. OK. It gives a critical value of chi-square. It gives a chi-square statistic of 148, which is way, way out beyond 7.8. So we should reject the null. It gives us a very, very small p-value. So I hope that helps. Just for the heck of it, you know how much I like to see the graphs of the distribution functions. I'm going to use StatCrunch to calculate the critical value of chi and also show us the graphs. So I'll go to Calculators, whoops, there's chi-square. We've got to put our degrees of freedom, which remember was the rows minus one times the columns, which was three, four minus one would be three. So three times one would be three. And we want always, in our hypothesis test, we're looking at the right tail. So I need to put in there our alpha, 0.05, and it draws the curve force that we can use. Calculator gives us our critical value, 7.18. And if you just checking, that's the same value that the pH stat gave us. So I just thought I would throw that in.