Spectrum sensing (SS) based on energy detection (ED) is a simple yet effective approach to detect the presence of unknown signals that are active in a specific band of frequencies. The classical ED (CED) algorithm uses the value of the energy detected in the current sensing slot as test statistic and has a fixed threshold, but improved signal detection performance is possible by modifying the test statistic and/or the detection threshold. In this paper we propose a novel ED algorithm for SS that considers a binary activity model for the signal to be detected and combines the use of an average energy test statistic with an adaptive decision threshold for improved detection performance. We present the analytical characterization of the proposed test statistic in terms of its mean and variance, and derive the expressions corresponding to the correct decision probability (CDP) and false alarm probability (FAP). Using the derived CDP and FAP expressions, we also determine the detection thresholds that yield desired values for the false alarm and missed detection probabilities. The proposed algorithm is illustrated with numerical results obtained from simulations, which confirm our theoretical findings and also show that the algorithm outperforms alternative adaptive ED algorithms.