 Hi, this is Dr. Don and I have a problem out of Chapter 9 on correlation. In this problem, we're given some raw data. We're given the weight of some vehicles and the braking distance in some vehicles. We're asked, can you conclude there's a significant linear correlation between vehicle weight and variability in braking distance on a dry surface with alpha 0.01? When I see this statement, can you conclude, that keys me that this is going to need a test of hypothesis. And for correlation, what we're testing is whether or not the population correlation coefficient rho is equal to zero or not. In this particular case, the claim is that it's significant, which means it's not equal to zero. Our alternative is rho not equal to zero. Our null is rho equal to zero. So this is a two-tail test. We first need to get the critical values of t. And again, because it's a two-tail, we'll have two values. To find it, let's use stat crunch. I'm going to go ahead and open up this data in stat crunch. So we'll have that to use in a minute. But we start with stat calculators t to get our critical values. We have one, two, three, four, five, six pairs. And the degrees of freedom for this type of test is n minus two, which means we've got a degrees of freedom of four. Our alpha is 0.01, and it's a two-tail, so we need to put half in each end. So that's 0.005, and I'm going to click Compute, and that gives us a critical value on the left side of minus 4.604. And on the upper side, we should have the same thing by symmetry, plus 4.604. So those are our critical values. Now you can calculate manually the t test statistic using those big, long formulas in Larson. Which you can do it faster in stat crunch. I'm going to go to stat, and we'll go down, and we're going to use regression. Remember correlation and regression are close cousins. Simple linear. Bring up the dialog box, and we'll select my x variable, my predictor, my y, my response variable. And here we want to perform the hypothesis test on both the intercept and the slope, which is what we're more interested in, the population slope row. And again, our alternative is not equal, and zero, which means we think the slope is not equal to zero. So we just click Compute, and we get our answers. I'm going to expand that there. You can see over here to the right, we've got our t test statistics for the slope. It's 1.606, and it has a p value of 0.184, which tells us that this is not statistically significant, because the p value is greater than alpha of 0.01. But we also want to check this test statistic, 1.606, against our critical area. And you can see that 1.606 is in here somewhere. It does not fall in the critical area on the right end or the left end. So that again says it's definitely not statistically significant. Therefore, we would conclude that the claim that there is a statistically significant slope row in the population cannot be supported. We would fail to reject the null.