Question: Infantile paralysis was linked to hygiene in a strange way that complicated the issue of parental consent. Children from generally high-income families were more likely to obtain consent to participate in the trials, but they were also more likely to contract the disease, because they had been raised in a cleaner environment where they were not exposed to antigens that would build up their immunity. Children from generally low-income families were less likely to obtain consent, and also less likely to contract the disease because of early exposure to antigens.
This theory could be tested by a case-control study in which equal numbers of infantile paralysis victims and nonvictims were randomly sampled to determine the proportions in each group that come from low-income families. If, in the general population (the nonvictim group), the proportion of low-income family children was 20%, what sample sizes would be needed to determine that the odds of contracting the disease for high-income family children was 3 times higher than for low-income family children? Compare the sample size requirements in this and the previous problem.