 Hi, this is Dr. Don and I have a problem out of chapter 10 on Chi Square. And in this particular problem, we want to know if the achieving a basic skill is related to the location of the school. And we're given some summary data over here that shows location, the variable, which is a categorical variable with two levels, urban and suburban. And then the subject variable with three levels, reading, math, and science. And we have our summary count data there. The claim in this case is that the variables are independent. And because that's a form of equality, that means the null is the claim. And those are our two hypotheses for this. And I'm going to wait to show you how to get the degrees of freedom and the critical value once we calculate the test statistic using StatCrunch. So let's do that now. I'm going to go over here and click on the little blue rectangle if you're in my StatLab. And then I'm going to open in StatCrunch and I'll see you there. Okay, StatCrunch open and it loaded the data correctly. Sometimes you need to check this to make sure that it lines it up properly. But here we have our row variable listed under location. And then our column variable, the type of course, listed in various columns. And then there's our summary data. We saw this using, of course, our stat path. And now this is going to be a contingency table. Remember, that's what we do with two-way chi-squares, contingency tables. So I select that and we have summary data. We don't have raw data. My column are the reading and I'll click on that. I'll hold down my control key, select math and science and make sure they populate over here on the right side. My row variables are in the location column. So I select that. Now you don't have to have any of these displayed. I like to get my expected count. And then I'm going to go down and click on chi-square test for independence, which is default, but I could double check anyway, who's going to leave the default confidence level of 95% for right now. And click OK. And we get our results. We get our expected values here in parentheses below the actual counts. And down in this table, we get our chi-square test statistic of 0.179 rounding the three places, p-value of 0.915 rounding the three places. And of course that would tell us not to reject the null. We would support the null. OK, now let's get the critical value. You can see that we're given the degrees of freedom. It's simple to find, but I just wanted to point out to you that stat crunch will give you the degrees of freedom for the chi-square. And we're going to go over here again to stat. This time to calculators, chi-square calculator. And for our problems, we're already always looking at the right tail. So I'm going to put that on the right side. We've got degrees of freedom of 2. We need to enter our alpha. Which is in this problem, it's 0.01 I think. And click compute. And we get our critical value. And the rejection area is to the right of 9.210 rounding to three places. And so that's how you can get this problem knocked out pretty quickly. The rejection region tells us not to reject the null since our test statistic is way down here. And of course our p-value tells us the same thing, do not reject the null. And therefore there is sufficient evidence to retain the claim, or not enough evidence to reject the claim, depends on the wording. Hope this helps.