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A wireless sensor network designed according to the sensor network with mobile agents (SENMA) architecture is engaged in a detection task, with a mobile agent (MA) that sequentially queries the networks nodes. The focus is on the effect of censoring: sensors respond to the query from the MA only if the local observations are deemed sufficiently informative; otherwise, they stay silent. Delivered data, if any, can be either unquantized or quantized to a single bit. The study is limited to shift-in-mean problems, involving two simple statistical hypotheses, where the noise distribution must be an even function but is otherwise arbitrary. Simple analytical relationships characterizing the tradeoff between the detection delay and the energy consumption of the network are derived, and examples of their applications are provided.