Summary. In group testing, the test unit consists of a group of individuals. If the group test is positive, then one or more individuals in the group are assumed to be positive. A group observation in binomial group testing can be, say, the test result (positive or negative) for a pool of blood samples that come from several different individuals. It has been shown that, when the proportion (p) of infected individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected. We extend the potential applications of group testing to hypothesis-testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable. Asymptotic relative efficiencies (AREs) of tests based on group testing versus the usual individual testing are obtained. The Pitman ARE strongly favors group testing in many cases. Small-sample results from simulation studies are given and are consistent with the large-sample (asymptotic) findings. We illustrate the potential advantages of group testing in hypothesis testing using HIV-1 seroprevalence data.