b} (3t) pts.) Suppose that a pharmaceutical company has asked you to work as a consultant on their CDVIDl'} vaccine project. They are planning to conduct a study to demonstrate that their vaccine candidate is more effective than the one Pfizer and BioNTech announced in early November ZED, which was stated to have efcacy of 90% against placebo in par ticipants without prior evidence of SARSCoVZ infection. They currently plan to enroll 2,[l{ltl participants, randomizing half to receive their vaccine candidate and half to receive the vaccine candidate from Pzer and BioNTech. They are interested in detecting a differ ence in proportions of at least 5% on the outcome of whether a patient becomes infected with SARSCoVE. The results of the trial will be analyzed with a twosided test. Previous dose-testing trials have been conducted to determine the lowest possible dose of virus sufficient for infecting most of those exposed; this will be the dosage used in the cur rent study. Participants in the study will be healthy volunteers ages lSB years who con sent to being deliberately exposed to the SARSCoVE virus in a controlled setting and have screened negative for risk factors associated with severe (SQUIDit}. Following exposure, any participants who test positive for the virus will be immediately treated with an antiviral drug. Studies that involve deliberate exposure of participants to an infectious disease are commonly referred to as challenge trials. \"You have been asked to conduct a simulation study to assess whether the study team has chosen an appropriate sample size. Based on discussions with the study team, you decide it seems feasible that they have identied a more effective vaccine and assign probability [135 to the alternative hypothesis. 1. Conduct a simulation incorporating your belief about the efficacy of the new vaccine candidate; be sure to clearly comment your code where necessary. In one paragraph, briey explain the general logic and organization of your simulation approach