Answer Happy

Placebo group Developing a COVID-19 vaccine is one of the most important scientific endeavors our of lifetime. In this exam, you will conduct a Bayesian analysis of the data produced by the clinical trial of the Moderna vaccinel. The data are: Vaccine group Infected Participants Infected Participants All patients 185 14,073 11 14,134 White 144 8,916 10 9,023 Communities of color 41 5,132 1 5,088 Let @ € (0.1) be the infection probability in group 9 € {placebo, vaccine} That is, a randomly selected person given the placebo has probability Opłacebo of contracting the virus, and a randomly-selected person given the vaccine has probability Ovaccine of contracting the virus. The efficacy of the vaccine if often defined as Ovaccine E=1- Oplacebo Say the objective of a study is to determine if the vaccine has efficacy at least E=0.7. The null hypothesis is E<0.7 and the alternative is E>0.7. Your analysis reveals that the posterior distribution of E is beta(10,1). Compute the posterior probability of each hypothesis and the Bayes factor. How much evidence does the Bayes factor provide in favor of the alternative hypothesis?