Point estimation of class prevalences in the presence of dataset shift has been a popular research topic for more than two decades. Less attention has been paid to the construction of confidence and prediction intervals for estimates of class prevalences. One little considered question is whether or not it is necessary for practical purposes to distinguish confidence and prediction intervals. Another question so far not yet conclusively answered is whether or not the discriminatory power of the classifier or score at the basis of an estimation method matters for the accuracy of the estimates of the class prevalences. This paper presents a simulation study aimed at shedding some light on these and other related questions.