A possible important environmental determinant of lung function in children is the 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, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. *8.31 What are the appropriate null and alternative hypoth- eses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hy- potheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the critical- value method. *8.34 Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke. *8.35 Assuming this is regarded as a pilot study, how many children are needed in each group (assuming equal num- bers in each group) to have a 95% chance of detecting a significant difference using a two-sided test with α = .05? *8.36 Answer the question in Problem 8.35 if the investiga- tors use a one-sided rather than a two-sided test.

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A possible important environmental determinant of lung
function in children is the 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, both of whose parents smoke, who have a mean

forced expiratory volume (FEV) of 2.1 L and a standard devia-
tion of 0.7 L; group 2 consists of 20 nonsmoking children of

comparable age, neither of whose parents smoke, who have
a mean FEV of 2.3 L and a standard deviation of 0.4 L.

*8.31 What are the appropriate null and alternative hypoth-
eses to compare the means of the two groups?

*8.32 What is the appropriate test procedure for the hy-
potheses in Problem 8.31?

*8.33 Carry out the test in Problem 8.32 using the critical-
value method.

*8.34 Provide a 95% CI for the true mean difference in FEV
between 5- to 9-year-old children whose parents smoke and
comparable children whose parents do not smoke.
*8.35 Assuming this is regarded as a pilot study, how many

children are needed in each group (assuming equal num-
bers in each group) to have a 95% chance of detecting a

significant difference using a two-sided test with α = .05?

*8.36 Answer the question in Problem 8.35 if the investiga-
tors use a one-sided rather than a two-sided test.

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