Although there is a plethora of methods to estimate sensitivity indices associated with individual inputs, there is much less work on interaction effects of every order, especially when it comes to make inferences about the true underlying values of the indices. To fill this gap, a method that allows one to make such inferences simultaneously from a Monte Carlo sample is given. One advantage of this method is its simplicity: it leverages the fact that Shapley effects and Sobol indices are only linear transformations of total indices, so that standard asymptotic theory suffices to get confidence intervals and to carry out statistical tests. To perform the numerical computations efficiently, Möbius inversion formulas are used, and linked to the fast Möbius transform algorithm. The method is illustrated on two dynamical systems, both with an application in life sciences: a Boolean network modeling a cellular decision-making process involving 12 inputs, and a system of ordinary differential equations modeling some population dynamics involving 10 inputs.