The negative effects of ambient air pollution on children's lung function has been well established, but less research is available about the impact of indoor air pollution. The authors of an article 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. Among the children in the study, 512 came from households that used coal for cooking or heating or both. Their FEV1 mean was 1423 with a standard deviation of 329. (A complex statistical procedure was used 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. (Round your answers to one decimal place.)

b)Suppose the investigators had made a rough guess of 330 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%? (Round your answer up to the nearest whole number.)