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 deviation 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 hypotheses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the criticalvalue method.
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A possible important environmental determinant of lung
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 deviation 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 hypotheses to compare the means of the two groups?
*8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31?
*8.33 Carry out the test in Problem 8.32 using the criticalvalue 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 numbers 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 investigators use a one-sided rather than a two-sided test.
Suppose 40 children, both of whose parents smoke, and
50 children, neither of whose parents smoke, are recruited
for the study.
*8.37 How much power would such a study have using a
two-sided test with significance level = .05, assuming that
the estimates of the population parameters in the pilot study
are correct?
*8.38 Answer Problem 8.37 assuming a one-sided rather
than a two-sided test is used.
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