3. New study data showed Pfizer's experimental Covid-19 pill, Paxloyid, was effective at keeping patients out of the hospital, but less adept at erasing milder symptoms often associated with breakthrough infections. Among the 428 patients who were randomly selected to receive Paxloyid, only 3 were hospitalized, compared to 10 hospitalizations among the 426 patients who were randomly selected to receive the placebo. a. What is the hospitalization rate for a patient who has received the Paxloyid treatment? For a patient who has received the placebo? [4] b. What is the average treatment effect of Paxloyid? [4] c. Construct a 95% confidence interval for the difference in hospitalization rate between the treatment group and the placebo group. (Hint: when two samples are independent to each other, the standard error for a difference between two proportions is given by: P-1 (1 - P1) , P2(1 - P2) SE = n1 n2 where p., and p, are the two proportions, n, and n1, are the size of the two samples, respectively.) [6] d. Is the effect of Paxloyid significant? [6]