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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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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