The negative effects of ambient air pollution on children’s lung function has been well established, but less research is available about the effects of indoor air pollution. The authors of “Indoor Air Pollution and Lung Function Growth Among Children in Four Chinese Cities” (Indoor Air, 2012: 3–11) investigated the relationship between indoor air pollution metrics and lung function growth among children ages 6–13 years living in four Chinese cities. For each subject in the study, the authors measured an important lung-capacity index known as FEV₁, the forced volume (in ml) of air that is exhaled in 1 second. Higher FEV1 values are associated with greater lung capacity. Burning coal inside houses can lead to increased levels of indoor air toxins that may have negative effects on lung function. Among the children in the study, 514 came from households that use coal for cooking or heating or both. Their FEV₁ mean was 1427 with standard deviation 325. (Using a complex statistical procedure the authors went on to show that burning coal had a clear negative effect on mean FEV₁ levels.)

a. Calculate and interpret a 95% (two-sided) confidence interval for true average FEV₁ level in the population of all children from which the sample was selected.

b. Suppose the investigators had made a rough guess of 320 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ml for a confidence level of 95%?