From the box formula for the standard error at the end of Section 10.1,
se(estimate 1 - estimate 2) =
√[se(estimate 1)]2 + [se(estimate 2)]2,
if you know the se for each of two independent estimates, you can find the se of their difference. This is useful, because often articles report a se for each sample mean or proportion, but not the se or a confidence interval for their difference. Many medical studies have used a large sample of subjects from Framingham, Massachusetts, who have been followed since 1948. A study (Annual of Internal Medicine, vol. 138, 2003, pp. 24–32) estimated the number of years of life lost by being obese and a smoker. For females of age 40, adjusting for other factors, the number of years of life left were estimated to have a mean of 46.3 (se = 0.6) for nonsmokers of normal weight and a mean of 33.0 (se = 1.8) for smokers who were obese. Construct a 95% confidence interval for the population mean number of years lost. Interpret.

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