In problem 19. We're going to be getting the critical regions and critical valleys for three different cases. So in the first case, he we given the non hypotheses me one equals mu to be called me. Three equals before and that gives us, uh a full different factors. So we can say C equals four seized. A number of factors were also given that and equals 18 and they never off significance. Lunder equals zero 0.5 So to get the critical region and critical value for this case scenario, we need to get the degrees of freedom for the numerator on for the denominator. So the degrees of freedom for the factors will be given by C minus one and the degrees of freedom. But the era will be given by and minus C. So this bets This occurs when into the numerator degrees of freedom and the denominator degrees of freedom. And in this case, the degrees of freedom will be equal to for minus one, which is three and 18 minus four, which is 14. So in this case, we need to get the F money that corresponds to three degrees of freedom for the new maritime, 14 degrees ing freedom for the denominator with the level of significance of Europe in here. If I So in this case the value will be three 14 and 0.5 So this will be the critical Bundy for F end from the Tibbles. It corresponds to the tree point 34 So the region the critical region, it's going to be elected using a bag room. This zero, this is one and this is 3.34 So we can share this area. Is there critical region for the first case? In the second case be we're tool that the non hyper this is his me one equals me to equal. Smith three equals beautiful equals mu five that queues this five doctors were also given that n equals 15 and the level of significance London zero 0.1 So, in the same way, we want to get the degrees of freedom. Um, and we'll have to get the degrees of freedom that's follows F A C minus one en may not see and our for which 0.1 in this case, it's going to be f C five minus one 15 minus Phi and zero point the Roban. So this would be if four degrees of freedom for the numerator and 10 degrees of freedom for the genome, Eaton and Europe in Terrebonne level of significance and from the table, this value equals five point name name. So this is the critical body. And so the critical region will be obtained a Swallow's zero. And this is one on this lease. Life won't name any. So we can should the critical region for bad case and lastly k c. We have They're not help with issues hitch not as me one equals mewtwo because mitri and that gives us three factors. We're also told that the sample size is 25 and equals 2 to 5. On the level of significance, he's 0.5 So we're going to follow the same procedure to get the critical value, and then we can determine the critical region. So in this case, the degrees of freedom for the new Meritor would be three minus one that sense that he's seem in this one. Then for the dinner militate Enman C, which is 25 minus three and then the level of significant 0.5 So this would be F 22 a 0.5 level of significance. And when you fine, you look for this value of the table, he will look teen 3.44 So the critical value is 3.44 And for the critical region, we have to do the same thing. How zero there and one here and 3.44 is mocked at So I should add Region is critical region for that case.