The Monte Carlo Bootstrap resampling method is among the most useful tools for accurate confidence interval computation. An inherent flaw of the method though, is its use of Monte Carlo resampling. Monte Carlo resampling relies on random resampling from the original sample in order to generate a confidence interval. Using random resampling, however, causes a method to yield different results nearly every time the method is performed on the same data. Further Monte Carlo resampling introduces simulation error. Simulation error occurs because for each draw each sample point has a 1/n probability of being chosen, and inevitably, some sample points randomly contribute to the sampling distribution more frequently than others. The Efficient Bootstrap Sample Design method for a sample of size n (EBSD(n)) has been created to address these inefficiencies inherent to the Monte Carlo Bootstrap1. EBSD(n) eliminates simulation error using principles of BIBD. The construction of this design allows for a fixed, systematic approach of constructing replicable confidence interval results. The motivation of this work was to compare the accuracy of confidence intervals applied on EBSD(n) to the accuracy of confidence intervals applied on the Monte Carlo Bootstrap. In order to do this, confidence interval methods type-1 error rate was computed for methods commonly applied on the Monte Carlo Bootstrap and for methods applied on EBSD(n). Two types of methods applied on EBSD(n) were tested for accuracy. (i) A new confidence interval method called E-skew and (ii) Confidence interval methods that are applied commonly on the Monte Carlo Bootstrap but instead were applied on EBSD(n). Both (i) and (ii) performed relatively accurately for specific types of probability distributions and statistics studied. Further, the new method E-skew was measured to be in statistically significant agreement with the BCa and Bootstrap-t algorithms using the Kappa statistic. This suggested E-skew could provide similar accuracy to these methods in a real data context while also benefitting from the advantages of EBSD(n).