Exact tests and confidence intervals are derived for the difference in failure intensities for two exponential populations, based on the conditional distribution of the total time-to-failure of one of the samples, given the total time-to-failure of the two samples. Moments of the distribution are studied, and approximate methods are discussed based on approximate percentiles and on the asymptotic normal distribution. An extension of the method to Type II censored samples is given, and an extension to the problem of comparing mean costs, when the costs of the products or failures are different, is also discussed.