 Hello, this is a video about conducting a test for independence during the entire hypothesis test. You are conducting a test to the claim that the row variable and column variable are dependent in the following contingency table. We want to find the test statistic and the p-value. So we need to go to Google Sheets and we need to put this data in there. In Google Sheets, you are going to go to the chi-square tab. In the chi-square tab, in B1, you'll have to drop down and you'll have to click independence because that's what we're conducting a test for independence. And then you'll start jotting down your data. You have your x column of data, y column of data, z column of data. Then you have your a row and then you have your b row. So go ahead and type in your data values, 37, 33, 31. Type in the next row is worth the data values. And then give Google Sheets some time to calculate. These formulas do take a while to calculate. So our test statistic is actually going to be appearing near chi-squared. Any time you run a test for independence, the distribution is actually a chi-square distribution. So it's not the bell-shaped normal distribution, it's the chi-square distribution. So we have our test statistic, chi-squared. It's about 18.652, we'll go ahead and we'll go to three decimal places. And then we have our p-value, which is the four decimal places 0.0001. So those are the two pieces of information they asked us for. So your test statistic, your chi-squared test statistic is 18.652 and then your p-value is 0.0001. So what does this mean? Well when you run a test for independence, the null hypothesis is always the row and column variables are independent. The alternative hypothesis is always the row and column variables are dependent. So what we're going to do is we're going to take our p-value and we're going to compare it to alpha, our significance level, 0.05. So that being said, it looks like we are less than alpha. So we reject H naught. So we reject H naught. So what this means is I can take my null hypothesis, cross that out, it has been rejected. Which means, guess what? This means that the row and column variables are dependent. They are dependent. So what this means is the following. Our claim was that the row and column variables were dependent, so it looks like our claim is true. So there is sufficient evidence to support the claim that the row and column variables are dependent. So that is how you conduct a test for independence. Thanks for watching.