Based on 11 separate studies, the Environmental Protection Agency (EPA) estimated that nonsmoking women who live with smokers have, on average, a 19 percent higher risk of lung cancer than similar women living in a smoke-free home. The EPA reported a 90 percent confidence interval for this estimate as 4 percent to 34 percent. After lawyers for tobacco companies argued that the EPA should have used a standard 95 percent confidence interval, a Wall Street Journal article reported “Although such a calculation wasn’t made, it might show, for instance, that passive smokers’ risk of lung cancer ranges from, say, 15% lower to 160% higher than the risk run by those in a smoke-free environment” [10].

a. Explain why, even without consulting a probability table, we know that a standard 95 percent confidence interval for this estimate does not range from −15 percent to +160 percent.

b. In calculating a 90 percent confidence interval, the EPA used a t distribution with 10 degrees of freedom. Use this same distribution to calculate a 95 percent confidence interval.