In a study of hand hygiene compliance in hospital surgical wards, researchers observed 375 instances for which hand washing would have been appropriate. Among the 375 observations, hands were washed only 161 times.16
(a) Using these data, a 95% confidence interval is (0.381, 0.481). Based on this interval, is it reasonable to conclude that the overall hand-washing rate at this surgical ward is less than 50%? Briefly explain.
(b) Over the period of observation of hand-washing opportunities in this study it is unlikely that more than 40 different doctors, nurses, and technicians were in the surgical ward. How might this information cast doubt regarding the validity of the confidence interval as an estimate of the proportion of workers who wash their hands?