Hey guys, my name is Colin and let's go ahead and jump right into this problem that deals with two different tests for tire wear and whether or not they may or may not be similar in result. So let's go ahead and first tackle part. They were asked to look at whether or not there is a that confidence interval that were given there is correct on DSO to do that. Of course, we're gonna start by finding our Alfa value. Since this is a 99% confidence interval, our confidence level is 99%. So our Alfa ends up being 0.1 and that means that are critical probability, which we calculate is one minus Alfa over to is just going to be one minus 10.0 1/2 or 0.995 and then the last kind of piece of information you know that we need for a T test is our degrees of freedom. We always calculate that is end the number of trials minus two since in this case, they mentioned that they ran that test on a random sample of 16 different tires. We know that our end is 16. So our degrees of freedom equals 16 minutes two or 14. So now we can go ahead and calculate our T statistic using Ah, those numbers that we just calculated. So we're going to be using a T statistic with an Alfa value of 0.1 and 14 degrees of freedom. And from the tea table chart, you can get that that is 2.977 So from this, we need to just go ahead now and calculate our margin of error, which we use our t statistic that we just found. And we multiply it by the standard error of the slope of the regression line, which in this case is 0.7104 When we multiply those two numbers together, we get a margin of error for our confidence interval as 0.211 for eight eso. Lastly, that construct that confidence interval. We're going to take thes slope of the regression line with 79021 from our many tab I'll put there and we're going to add and subtract points to one one for eight. And when we do that, we get a 90 99% confidence interval that matches the one. Not that we were getting a problem. 0.57 85 and the upper boundary is 1.0 one. And so now we're asked to look at different tests. So Part B s whether or not researchers that use that test there where we've got the null hypothesis as beta equals one and alternative hypothesis is beta is not equal to one whether or not that's an acceptable test to run. And, uh, I would say that this isn't appropriate pair of hypotheses, because if the tests yielded the same output, the two different tests showed the same output for each value or for each tire. Then that slope would be one. Um and so this is a good test to see if there is a difference between the two or not. Because if there is a difference that will be able to reject that null hypothesis, and if we can't of them will have to say that there is not sufficient evidence. So basically, we're looking to see whether or not beta equals one is statistically significant. And to do that, uh, that's kind of the lead in here to part C. We're asked to look at our confidence interval, which I'll remind you from. We calculated that down in part a that conference animals 0.5785 to 1.1 I mean, this is important because you'll see that this actually contains zero. And so because our 99% confidence interval contains zero, we cannot reject the null hypothesis. So we do not reject, which means that we cannot say that there is sufficient evidence to support the claim of a difference between the two tests we cannot reject. H not and cannot from this test anyway say that there is a statistically significant difference between the two tests.