Data assimilation methods have recently been implemented in the sensitivity analysis and uncertainty quantification tool SHARK-X. This paper presents how they were used with sensitivity coefficients and randomly-sampled nuclear data to simulate integral parameters from the LWR-PROTEUS Phase II experiment. The adjusted calculated values of the integral parameters showed small differences between the two implemented data assimilation methods, GLLS and MOCABA. The differences were statistically significant, but were caused by round-off errors. The experiment was also analyzed to search for sources of bias in the simulations. Analysis of the chi-squared parameter showed that many of the integral parameters have biases that were inconsistent with their high correlation. This indicates that the bias likely arose from sources other than nuclear data, like the modeling of the fuel burnup, the 2D model in CASMO-5M, or from experimental methods. The nuclear data adjustments were analyzed and ranked according to how they improved the computational bias and reduced its uncertainty.