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.