A possible important environmental determinant of lung function in children is amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5-9 years of age with two parents who smoke, and have mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, with two parents who do not smoke, and have mean FEV of 2.3 L and a standard deviation of 0.4 L. You may assume that the distribution of FEV is approximately symmetric in both groups.

a) Do the children of two parents who smoke have mean FEV different from the children of two parents who do not smoke? Conduct a formal hypothesis test. Use the min(n1 1, n2 1) approximation for the degrees of freedom.

b) Summarize the findings in language that someone who has not taken a statistics course would understand, referencing specific details from the analysis as needed.

c) Suppose you have been asked to assess the design of a new study addressing the same ques- tion. In the new study, researchers plan to recruit 20 nonsmoking children 5-9 years of age with two parents who smoke and 20 nonsmoking children 5-9 years of age with two parents who do not smoke; children will be matched based on similar household income. Briefly ex- plain whether you believe the new study has more potential to show an association between smoke exposure and lung function than the original study.