A test for Lyme disease will be positive with probability 0.9 for a person who has Lyme, and with probability 0.05 for a person who does not have Lyme. You plan to test Ho: "no Lyme" vs. H1 : "Lyme" by taking the test. Define the parameter 0 to represent your Lyme status, with 0 = 0. if "no Lyme" and 0 = 01 if "Lyme", and the data X to be an indicator for a positive test outcome, with X = 1 for a positive test and X = 0 for a negative test. a) What is the significance level a for a test that rejects if X = 1? What is the power of this test? b) For a Bayesian approach, assume prior probabilities P(0 = 0) = Po and P(0 = 01) = 1 -Po and find an expression for P(0 = 0.|X = 1) in terms of po. c) The significance level a is often mistakenly interpreted as the probability Ho is true, given the data. The CDC estimates a 1% probability of Lyme transmission from a deer bite, so it might make sense to assume po = 0.99 as a prior probability if you had a deer tick bite but no Lyme symtoms. Compute P(0 = 0.|X = 1) assuming po = 0.99. Also state the conditional probability represented by a in this context