Underestimation of the sample size given by using Eq. (5) (Table 1A).

Table 1A. Preliminary sample size (, number of required positive pools) for estimating the population proportion, computed with Eq. (5) and three sample size increments (, , and ) with their corresponding probability that the confidence interval width is smaller than the specified value (), computed with Eq. (6). For a 95% CI and , is the desired CI width. is the probability that (W) is smaller than the specified value () calculated using Eq. (6). Table 1B. Proportion of times the MLE of p is greater than the population proportion for different combinations of values of and that produce simulated 40, 000 samples. Table 1C. Mean Square Error for 40, 000 simulated samples with and different values of and .