Q2 (10 points) Early Bird Diagnostic Tests (EB) prides itself on getting its tests to market as quickly as possible, even if they're not as effective as they could be, and then improving them later on. Twice As Nice Diagnostic Tests (TAN) likes to market their diagnostic tests as being as effective as using its competitor's tests twice. Both companies measure the quality of their diagnostic tests by entirely focusing on their positive predictive value (PPV), i.e., the probability of a person actually having the condition given that they've received a positive diagnostic test. EB put out a particular diagnostic test with a sensitivity of 60% and a specificity of 90% for a condition which 6% of the population currently have. (You should use this value as your prior.) (a) What sensitivity and specificity should TAN want for their diagnostic test so that the PPV of the TAN test is the same as if the person had received two positive EB tests? b) Now EB knows they need to improve their diagnostic test to remain competitive. They are considering two different formulations, Formula A which would improve the sensitivity from 60% to 99%, or Formula B which would improve the specificity from 90% to 99%. Which formulation will make EB's new and improved diagnostic test have a better PPV than TAN's test? Q2 (10 points) Early Bird Diagnostic Tests (EB) prides itself on getting its tests to market as quickly as possible, even if they're not as effective as they could be, and then improving them later on. Twice As Nice Diagnostic Tests (TAN) likes to market their diagnostic tests as being as effective as using its competitor's tests twice. Both companies measure the quality of their diagnostic tests by entirely focusing on their positive predictive value (PPV), i.e., the probability of a person actually having the condition given that they've received a positive diagnostic test. EB put out a particular diagnostic test with a sensitivity of 60% and a specificity of 90% for a condition which 6% of the population currently have. (You should use this value as your prior.) (a) What sensitivity and specificity should TAN want for their diagnostic test so that the PPV of the TAN test is the same as if the person had received two positive EB tests? b) Now EB knows they need to improve their diagnostic test to remain competitive. They are considering two different formulations, Formula A which would improve the sensitivity from 60% to 99%, or Formula B which would improve the specificity from 90% to 99%. Which formulation will make EB's new and improved diagnostic test have a better PPV than TAN's test