0" & O | Mao x| @ mygo x | B Signot x | i Home x | & Mail- x | i Conte x 20183 x | [ sCE1 x | & chat6 x | Applic x| downl X | he @860 x | + = o X G Q. A https://learn-ap-southeast-2-prod-fleet01-xythos.content blackboardcdn.com/5ddb108fe0c42/291833107X-Blackboard-S3-Bucket=learn-ap-southeast-2-prod-fleet0... {7 ED = QJ'Q@ 9 0 v Daw v & AN | @b | Ask Copilot - + 3 | ofa | R | B Q| @ ' 3 | Editwith Acobat Q CURTE @ O GUICTATe JIo0 an YOl aiisWer. (10 YOI are mor Sure oW 06 00 Cis S g, check out the examples in the notebooks under the linear programming folder inside the - S LABS page in the LMS.) 3. Do the following exercises on hypothesis testing. In each case, prepare an answer that includes & the following: a statement of both the null and the alternative hypothe deseription of the test statistic used; the rejection region defined in terms of the critical statistic value (and also m indicate how you will the p-value for your sample here); and the conclusion from the hypothesis test. Use probabilities caleulated using the binomial distribution to answer the questions, not a normal or other approximation to it. Assume the level of significance () used for the tests + is 0.05. (16 marks) a) Two political parties (A and B) are active in a district. In the last election, public sup- port for party B stood at 48%. Each party has been working hard since to lure voters away from its rival. The leader for party B has hired you to find out if there is evidence that its efforts are paying off. Suppose you take a random sample of 120 voters and 69 say they support B. Would you conclude that the level of support for B is now higher than 48%? b Health experts suspect that a new variant of a virus has a different infection rate. The old variant of the virus had an infection rate of 40%, i.e. 40% of contacts between an infected and non-infected person result in an infection. You have been asked to help determine if the new variant has a different infection rate. Suppose you examined a sample of contact tracing data and found that out of 100 eontact s 32 resulted in infections. Conduct a statistical test to determine if your empirical evidence supports the claim that the probability of a contact resulting in an infection is now different from 40%. 4. The Testmax Company manufactures testing devices. Its current daily production is 200 units of TMx-300 and TMx-330 devices. The company wants to know if profits could be increased by changing the product mix. The table below presents information on the hours required to build each device type and the production capacities of the four departments in the manufacturing plant. What product mix would maximise total net profit? Use linear programming to solve the problem. (16 marks) a) Write out the mathematical formulation of the LP problem (objective function and con- straints)