4. On May 1, the FDA granted an 'emergency use authorization' for clinicians to use the experimental drug, called Remdesivir, in hospitals for people with severe COVID-19. (a) (3pts) Gilead (Remdesivir manufacturer) announced that in its own clinical trial, more than half of 400 participants with severe COVID-19 had recovered from their illness within two weeks of receiving Remdesivir. But the study failed to include a control group (participants taking a placebo), making the results difficult to interpret. Why is it important to include a control group in the study? Explain. (b) (8pts) On April 29, Anthony Fauci, the director of NIAID (National Institute of Allergy and Infectious Diseases), announced that a clinical trial had showed that 22 people taking Remdesivir recovered in 11 days on average (standard deviation 7.3 days), compared to 15 days on average (standard deviation 7.8 days) for 18 people on a placebo. Is there convincing evidence that Remdesivir could shorten the time to recovery from coronavirus infection? Conduct a test at a 5% significance level. Show all 5 steps properly