Smartphone users' decisions about whether to attend to a notification after sensing it are under-researched. We therefore studied 33 Android users, and found that they speculated extensively about notifications' sources-i.e., which apps and which senders were responsible for them-before attending to them. The participants' speculation about apps was both more common and more accurate than that about senders. They also were more likely to 1) perceive notifications as important, 2) attend to them, and 3) consider them beneficial if they speculated about them than if they did not or could not. Participants' speculations were based on the alert's inherent characteristics, context, and temporality. Inaccurate speculations were mainly caused by unclear signals, insufficient clues, and a multiplicity of possible sources. Ringer mode affected the accuracy of user speculation, but not its frequency or the frequency of attending to notifications.