The estimate of scope economies is a nonlinear combination of estimated coefficients from an empirical model. This estimate usually involves out-of-sample predictions when calculating the separated costs (as a part of calculation of scope economies). These difficulties make it hard to give the precise prediction and to calculate the standard deviation of this estimate along with its confidence intervals. In this paper, we demonstrate methods for constructing confidence interval for scope economies to allow researchers to draw inferences from estimated economies of scope. We review the common approaches such as delta method or bootstrap adopted by previous studies. In contrast of the above approximation methods, this study also proposes an alternative method, Bayesian approach, to produce full predictive distribution for this measure with posterior distribution. To demonstrate these three approaches, we use a balanced panel data including 37 Australian public universities over the period 2003-12. All three approaches use a quadratic cost function with two outputs.Estimates of scope economies will be calculated with the sample data and estimated parameters from the model. Results shows that our Bayesian approach gives the most precise (the least standard deviations) among all approaches.