A recent study showed that correctly administered rapid antigen tests (RATs) will return a positive result 65.3% of the time among patients that have a COVID infection. What is the implied false negative "rate" for these tests?Group of answer choices0.9990.3470.6530.001

As of October 2023 the current prevalence of Covid-19 in New South Wales is estimated to be roughly 1 in 1,000. Suppose a Rapid Antigen test has a 95% chance of correctly identifying someone with the virus and a 98% chance of correctly identifying someone without the virus. If we made all 8,000,000 people in New South Wales take a Rapid Antigen test what percentage of the people who tested positive would actually have Covid-19?Group of answer choices0.1%95%2.5%2%5.5%4.5%

. A gene test shows promising results in providing early detection for colon cancer. However, 5% of all test results are falsely positive; that is, results indicate that cancer is present when the patient is, in fact, cancer-free. Given this false positive rate, how many people out of 10,000 would have a false positive result and be alarmed unnecessarily?

Which of the following is used to distinguish the false positive rate from the false negative rate?1 pointSpecificityNegative Predictive ValueFalse NegativeSensitivity

Researchers at a large pharmaceutical company are conducting a clinic trial to determine the effectiveness of a new therapeutic for COVID-19. Patients are recruited for the clinical trial immediately following a positive test result for COVID-19. Half of the patients, assigned at random, will receive the new therapeutic. The other half will receive an off-label therapeutic currently in wide use by a subset of all doctors treating COVID-19 patients. Patients will be tested daily and the number of days between the initial positive test result and a negative test result are recorded. Assuming that all conditions for inference are met, which of the following significance tests should be conducted to determine whether the use of the new COVID-19 therapeutic results in a smaller average number of days until a negative test than the widely used off-label therapeutic? (A) Paired t-test, one-sided (B) Two-sample z-test, one-sided (C) Two-sample z-test, two-sided (D) Two-sample t-test, one-sided (E) Two-sample t-test, two-sided

1. The HIV test we consider is an enzyme-linked immunosorbent assay, commonly known as an ELISA. ELISA’s true positive rate, also referred to as sensitively, is estimated as 𝑃(𝐸𝐿𝐼𝑆𝐴 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒|𝑃𝑒𝑟𝑠𝑜𝑛 𝑡𝑒𝑠𝑡𝑒𝑑 ℎ𝑎𝑠 𝐻𝐼𝑉 ) = 0.93. Its true negative rate, also referred to as specificity, is estimated as 𝑃(𝐸𝐿𝐼𝑆𝐴 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒|𝑃𝑒𝑟𝑠𝑜𝑛 𝑡𝑒𝑠𝑡𝑒𝑑 𝑛𝑜 𝐻𝐼𝑉 ) = 0.99. Also, the prevalence of HIV in the overall population, which is estimated to be 1.48 out of every 1000 American adults. i.e. 𝑃(𝑃𝑒𝑟𝑠𝑜𝑛 𝑡𝑒𝑠𝑡𝑒𝑑 ℎ𝑎𝑠 𝐻𝐼𝑉) = 0.00148.i. Compute the probability that someone has HIV if ELISA tests positive.ii. What is the probability that someone who tests positive does not have HIV?iii. What is the probability of being HIV positive if the second ELISA test comes back positive?iv. What is the probability that one has HIV after testing positive three times on the ELISA test?(Assume that all three ELISAs are independent)