In this paper, surrogate based approaches for multifidelity uncertainty quantification are implemented in a sonic boom prediction framework for improving the supersonic aircraft design process under uncertainties. The sonic boom prediction framework requires output from multidisciplinary analyses such as obtaining the flow field pressure distribution solution from a flow solver to generate the near-field pressure signature of the aircraft and then propagating this near-field pressure signature throughout the atmosphere to the ground by using aeroacoustic methods. The open-source SU2 suite is employed as a high fidelity flow analysis tool to obtain the aerodynamic solution while in-house post-processing scripts are developed to generate the necessary near-field pressure signature. For low-fidelity flow analysis, A502 PANAIR, a higher-order panel code to solve flows around slender bodies in low angles of attack for subsonic and supersonic regimes, is used. For nonlinear aeroacoustic propagation, NASA Langley Research Center code sBOOM is incorporated with the near-field pressure signature for enabling both high-fidelity and low-fidelity sonic boom calculations. Efficient uncertainty quantification tools are developed in-house by implementing multifidelity polynomial chaos expansion and multifidelity Monte Carlo methods. Several atmospheric parameters are considered to comprise randomness and these uncertainties are propagated into the sonic boom loudness prediction of a low boom aircraft called the JAXA wing-body. Finally, an assessment of multifidelity uncertainty quantification methods is presented in terms of their performances and numerical accuracies.