Trade-Off Between Sample Size and Accuracy: Case of Measurements under Interval Uncertainty

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy:first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional measurements can improve the accuracy of the result of this series of measurements;second, we can replace the current measuring instrument with a more accurate one; correspondingly, we can use a more accurate (and more expensive) measurement procedure provided by a measuring lab -- e.g., a procedure that includes the use of a higher quality reagent.In general, we can combine these two ways, and make repeated measurements with a more accurate measuring instrument. What is the appropriate trade-off between sample size and accuracy? This is the general problem that we address in this paper.