10.123 Standard error of difference From the box formula for the standard error at the end of Section 10.1,

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se (estimate 1 estimate 2) = V[se (estimate 1)] + [se (estimate 2)], if you know the se for each of two independent es- timates, you can find the se of their difference. This is useful because often articles report an se for each sample mean or proportion, but not the se or a con- fidence 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.