In this paper, we consider a cognitive multiple access channel (MAC) in which the secondary users seek to communicate with the secondary base station in a spectrum-sharing environment. The base station selects only one secondary user, which maximizes the weighted difference between the channel power gains of the interference link and the cognitive transmission link. This selection strategy can also be specialized to selecting the secondary user that has either the least interference channel gain or the highest data channel gain. Consequently, the selected secondary user is subject to an interference power constraint in order to avoid harmful interference inflicted on the primary user. It is assumed that the primary user and secondary users operate under statistical quality of service (QoS) constraints imposed as limitations on the buffer size. In this setting, we characterize the effective capacity for both primary user and the secondary users under different selection methods. The impacts of the secondary user selection method, the number of secondary users, QoS constraints on the performance of both the primary user and secondary users are investigated. We interestingly show that for a large number of secondary users, the performance of the primary user is not affected by the selection method in the interference-limited regime.