### Educational Content: Understanding FEV₁ Level Analysis#### BackgroundThe negative effects of ambient air pollution on children's lung capacity have been well-established. Recent research seeks to understand the impact of indoor air pollution, specifically the use of household coal for heating and cooking, on children's lung health.#### Study SummaryThe study measures Forced Expiratory Volume in one second (FEV₁), which is an important indicator of lung capacity. Among the children in the study, the average FEV₁ was reported as 142 with a standard deviation of 325 from a sample of 516 children. #### Analytical FocusThe study aims to determine whether the burning of coal in households has a negative effect on the mean FEV₁ levels across the broader population of children.#### Statistical Analysis##### Part (a)- **Task:** Calculate and interpret a 95% confidence interval for the true average FEV₁ level.- **Result (Round to one decimal place):** [Calculation Required]##### Interpretation OptionsPlease select the correct interpretation of the confidence interval:1. We are 95% confident that this interval does not contain the true population mean.2. We are 95% confident that the true population mean lies above this interval.3. We are 95% confident that the true population mean lies below this interval.4. We are 95% confident that this interval contains the true population mean.5. Does it appear that the parameter of interest has been accurately estimated?- Evaluate whether the width of the interval is narrow or wide in relation to the scale of the data.##### Part (b)- **Task:** Given a rough estimate of 320 for the FEV₁ value before data collection, determine the necessary sample size to achieve an interval width of 40 for a 95% confidence level.- **Result (Round to nearest whole number):** [Calculation Required]### ConclusionThis analysis provides insight into the statistical approach to evaluating the effects of indoor air pollution on children's lung function. Understanding the calculation and interpretation of confidence intervals is crucial for assessing the reliability of study findings and formulating public health policies.

Want to calculate a 95% confidence interval for the meanThe confidence interval for the mean is…

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, 516 came from households that used coal for cooking or heating or both. Their FEV₁ mean was 1427 with a standard deviation of 325. (A complex statistical procedure was used to show that burning coal had a clear negative effect on mean FEV, levels.) (a) Calculate and interpret a 95% (two-sided) confidence interval for true average FEV, level in the population of all children from which the sample was selected. (Round your answers to one decimal place.) Interpret the resulting interval. We are 95% confident that this interval does not contain the true population mean. We are 95% confident that the true population mean lies above this interval. We are 95% confident that this interval contains the true population mean. We are 95% confident that the true population mean lies below this interval. Does it appear that the parameter of interest has been accurately estimated? O 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. 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. 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. 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. (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%? (Round your answer up to the nearest whole number.)