This paper examines a test for the hypothesis of weak dependence, whose limit distribution, G(z), is a Gumbel distribution which appears as one of the three possible limit distributions in the theory of extreme-values. However, since G(z) may be a poor approximation to the finite sample distribution, the rate of convergence being logarithmic, see Hall (1979), inferences based on G(z) may not be very reliable for moderate sample sizes. For that reason, we describe an approach to bootstrapping the test based on a naive, e.g. Efron (1979), resampling of the data. We show that the bootstrap principle is consistent under very mild regularity conditions. This can be quite surprising since Efron's resampling scheme is generally inconsistent under dependence.