The generalized estimating equation (GEE) approach is widely used in regression analyses with correlated response data. Under mild conditions, the resulting regression coefficient estimator is consistent and asymptotically normal with its variance being consistently estimated by the so-called sandwich estimator. Statistical inference is thus accomplished by using the asymptotic Wald chi-squared test. However, it has been noted in the literature that for small samples the sandwich estimator may not perform well and may lead to much inflated type I errors for the Wald chi-squared test. Here we propose using an approximate t- or F-test that takes account of the variability of the sandwich estimator. The level of type I error of the proposed t- or F-test is guaranteed to be no larger than that of the Wald chi-squared test. The satisfactory performance of the proposed new tests is confirmed in a simulation study. Our proposal also has some advantages when compared with other new approaches based on direct modifications of the sandwich estimator, including the one that corrects the downward bias of the sandwich estimator. In addition to hypothesis testing, our result has a clear implication on constructing Wald-type confidence intervals or regions.