Babies 6 to 23 months of age with inner ear infections were given antibiotics. The children were randomly assigned to receive antibiotics for a full 10 days or to receive antibiotics for 5 days and then a placebo for 5 days. There were 229 children assigned the shorter course, and 77 of them had “clinical failure” whereas of the 238 assigned to the longer course of antibiotics, 39 had clinical failure. (Hoberman et al., “Shortened antimicrobial treatment for acute otitis media in young children,” New England Journal of Medicine, vol. 375 [December 2016]: 2446–2456) 

a. Compare the percentage of clinical failure in each group and state which group did better.

b. Create a two-way table with 10 days and 5 days across the top and failure and success down the left side. Fill in all four numbers. 

c. Was this an observational study or a controlled experiment? How do you know? 

d. Can you conclude that the treatment caused the difference? Why or why not?