Vermin is an infection with the worm Enterobius vermicularis that usually occurs in children aged 5 to 10 years. Worldwide, the annual incidence is around 200 million. In the autumn of 2022, Ummarino and colleagues published an article in Frontiers in Microbiology where they presented a new PCR-based method for detecting children's disease. Of a total of 27 patients who had placenta, 24 tested positive with the new method. Of a total of 27 patients who did not have placenta, there were 27 patients who received negative tests with the new method. a. What is the sensitivity and specificity of the new test? Show calculation. In a kindergarten, we assume that 10% of the children have children's land. b. Set up a probability tree for the probability of infection and different test results if all the children in the nursery are tested. c. What is the probability that a random kindergarten child will get a positive answer to the test? Show calculation. d. What is the positive predictive value (PPV), i.e. the probability that a kindergarten child with a positive test actually has genital warts? e. What is the negative predictive value (NPV), which is the probability that a child with a negative test does not actually have placenta? Some suggest that you only need to test children who have symptoms (anal itching). Among these children, we assume that 40% have children. Among children without symptoms, we assume that the probability of having birth defects is zero. f. Now what is the probability that a random kindergarten child gets a positive answer to the test, and what is the probability that a random kindergarten child gets a negative answer? Show calculation. g. What are the PPV and NPV with these new assumptions? Show calculation. h. Compare PPV and NPV with corresponding values from e). Explain the relationship between those PPVs. Which strategy would you choose (test everyone or test those with symptoms)? Justify the answers.