Question: In Exercise, a study is described in which the mean IQs at age 4 for children of smokers (at least ten cigarettes a day) and nonsmokers were compared. The mean for the children of the 66 nonsmokers was 113.28 points, while for the children of the 47 smokers it was 103.12 points. Assume that the pooled standard deviation for the two samples is 13.5 points and that a pooled t-test is appropriate. Test the hypothesis that the population mean IQ at age 4 is the same for children of smokers and of nonsmokers versus the alternative that it is higher for children of nonsmokers. Use a = .01.
Exercise: A study was conducted on pregnant women and the subsequent development of their children (Olds et al., 1994). One of the questions of interest was whether the IQ of children would differ for mothers who smoked at least 10 cigarettes a day during pregnancy and those who did not smoke at all. The mean IQ at age 4 for the children of the 66 nonsmokers was 113.28 points, while for the children of the 47 smokers, it was 103.12 points. The standard deviations were not reported, but from other information that was provided, the pooled standard deviation was about 13.5 points.
a. Assuming that these women and children are a representative sample, find a 95% confidence interval (use t*) for the difference in mean IQ scores at age 4 for children of mothers who do not smoke during pregnancy and those whose mothers smoke at least 10 cigarettes a day during pregnancy. Write a sentence interpreting the interval.
b. One of the statements in the article was "after control for confounding background variables the average difference observed at 36 and 48 months was reduced to 4.35 points (95% CI: .02, 8.68)" (Olds et al., 1994, p. 224). Explain the purpose of this statement, and interpret the result given.