Despite other comments that are somewhat aghast at the idea of dictating a margin of error, the threshold at which you consider something significant IS arbitrary. The 'p' value of 0.05, the inverse of the '95%'confidence interval, is commonly chosen by researchers but is by no means the only choice you could make. Some research uses less stringent or more stringent thresholds, depending on the nature of the research and the assumptions of the researchers.