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 1421 with a standard deviation of 325. (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.
1) Interpret the resulting interval.
a) we are 95% confident that this interval contains the true population mean.
b) we are 95% confident that the true population mean lies below this interval.
c) we are 95% confident that this interval does not contain the true population mean.
d) we are 95% confident that the true population mean lies above this interval.
2) Does it appear that the parameter of interest has been accurately estimated?
A) This interval is quite narrow relative to the scale of the data values themselves, so it could be argued that the mean has not been accurately estimated.
B) This interval is quite narrow relative to the scale of the data values themselves, so it could be argued that the mean has been accurately estimated.
C) This interval is quite wide relative to the scale of the data values themselves, so it could be argued that the mean has been accurately estimated.
D) This interval is quite wide relative to the scale of the data values themselves, so it could be argued that the mean has not been accurately estimated.
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 40 ml for a confidence level of 95%?