A study of 6,839,854 births in the United States found a total of 6522 babies were born with a finger defect, either syndactyly (fused fingers), polydactyly (extra fingers), or adactyly (fewer than five fingers). Researchers examined 5171 of these babies with finger defects in further detail. Of these babies, 4366 had mothers who did not smoke while pregnant, and the rest had mothers who did smoke while pregnant. In a sample of 10,342 babies from the population with normal fingers, 9062 of their mothers did not smoke while pregnant, while mothers of the remaining 1280 did smoke while pregnant. Answer the following questions to establish the magnitude of the effect of smoking on the occurrence of finger defects.

a. Why is this considered to be an observational study rather than experimental? What type of observational study is it?

b. Use a graph to show the association between smoking during pregnancy and finger defects.

c. What is the 95% confidence interval for the proportion of babies born in the United States with one of these finger defects? Is the defect common or rare?

d. What is the odds ratio of these birth defects, comparing smoking to nonsmoking mothers? Provide a 95% confidence interval for the odds ratio. Based on your results, which group of mothers has the higher odds of having a child with a finger defect?

e. Is it justified to consider your estimate of odds ratio in part (d) also to be an estimate of the relative risk? Explain.