The chemical benzalkonium chloride (BAC) is an antibacterial agent that is added to some asthma medications to prevent contamination. Researchers at the University Of Florida College Of Pharmacy have discovered that adding BAC to asthma drugs can cause airway constriction in patients. In a sample of 18 asthmatic patients, each of whom received a heavy dose of BAC, 10 experienced a significant drop in breathing capacity. Based on this information, a 95% confidence interval for the true percentage of asthmatic patients who experience breathing difficulties after taking BAC is (.326, .785).
a. Why might the confidence interval lead to an erroneous inference?
b. How many asthma patients must be included in the study in order to estimate the true percentage who experience a significant drop in breathing capacity to within 4% with a 95% confidence interval?