In this paper we consider the use of bootstrap methods to compute interval estimates and perform hypothesis tests for decomposable measures of economic inequality. Two applications of this approach, using the Gini coefficient and Theil's entropy measures of inequality, are provided. Our first application employs pre- and post-tax aggregate state income data, constructed from the Panel Study of Income Dynamics. We find that although casual observation of the inequality measures suggests that the post-tax distribution of income is less equal among states than pre-tax income, none of these observed differences are statistically significant at the 10% level. Our second application uses the National Longitudinal Survey of Youth data to study youth inequality. We find that youth inequality decreases as the cohort ages, but between age-group inequality has increased in the latter half of the 1980s. The results suggest that (1) statistical inference is essential even when large samples are available, and (2) the bootstrap procedure appears to perform well in this setting.