What is the legal test for discharging a juror from a trial where the defense counsel alleges that the juror was dozing?

As we recently observed, "[a] trial court may discharge a juror who 'becomes ill, or upon other good cause shown to the court is found to be unable to perform his [or her] duty, ...' ( 1089, 5th par.) Once a trial court is put on notice that good cause to discharge a juror may exist, it is the court's duty 'to make whatever inquiry is reasonably necessary' to determine whether the juror should be discharged. [Citation.] We have recently explained, however, that the mere suggestion of juror 'inattention' does not require a formal hearing disrupting the trial of a case. [Citation.]" (People v. Espinoza (1992) 3 Cal.4th 806, 821, 12 Cal.Rptr.2d 682, 838 P.2d 204.)

" 'The decision whether to investigate the possibility of juror bias, incompetence, or misconduct--like the ultimate decision to retain or discharge a juror--rests within the sound discretion of the trial court. [Citation.] The court does not abuse its discretion simply because it fails to investigate any and all new information obtained about a juror during trial.' " (People v. Osband, supra, 13 Cal.4th 622, 675-676, 55 Cal.Rptr.2d 26, 919 P.2d 640.) A hearing is required only where the court possesses information which, if proved to be true, would constitute "good cause" to doubt a juror's ability to perform his or her duties and would justify his or her removal from the case. (Ibid.)

In People v. Espinoza, supra, 3 Cal.4th 806, 821, 12 Cal.Rptr.2d 682, 838 P.2d 204, we concluded that defense counsel's speculation that a juror might have been sleeping was insufficient to apprise the trial court that good cause might exist to discharge the juror, and therefore did not obligate the court to conduct any further inquiry. In People v. DeSantis (1992) 2 Cal.4th 1198, 1233-1234, 9 Cal.Rptr.2d 628, 831 P.2d 1210, we concluded that the trial court's "self-directed inquiry," which involved observing several jurors closely to determine whether they were asleep, and determining that none was dozing, was sufficient, and that a more formal hearing was not required under the circumstances.