An important disadvantage of the h-index is that typically it cannot take into account the specific field of research of a researcher. Usually sample point estimates of the average and median h-index values for the various fields are reported that are highly variable and dependent of the specific samples and it would be useful to provide confidence intervals of prediction accuracy. In this paper we apply the non-parametric bootstrap technique for constructing confidence intervals for the h-index for different fields of research. In this way no specific assumptions about the distribution of the empirical h-index are required as well as no large samples since that the methodology is based on resampling from the initial sample. The results of the analysis showed important differences between the various fields. The performance of the bootstrap intervals for the mean and median h-index for most fields seems to be rather satisfactory as revealed by the performed simulation.