The point estimate of economies of scope is a nonlinear combination of estimated coefficients from an empirical model. This estimate usually involves out-of-sample predictions when calculating the separate costs (as a part of the calculation of economies of scope). 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 the confidence interval for economies of scope 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 to the above approximation methods, this study also proposes an alternative method, Bayesian approach, to produce full predictive distribution for this measure with the posterior distribution. To demonstrate these three approaches, we use a balanced panel data including 37 Australian public universities over the period 2003-12. Our Bayesian approach uses a quadratic cost function with two outputs. Estimates of economies of scope will be calculated with the sample data and estimated parameters from the model.