There are Frequentist and Bayesian tests that can be done for the sample, to test whether one level within an attribute is higher than another.
For the Frequentist tests, one typically uses the normalized (zero-centered diffs) individual-level output. One runs a matched pairs t-test.
For the Bayesian tests, one typically examines the "alpha draws" file which contains the estimates of the population mean utilities across iterations of the HB algorithm. One typically ignores the first 5K or 10K draws focuses only on the draws after that (after convergence is assumed). Counting the draws to observe what % of the draws indicate that one level of an attribute is higher than another level within the same attribute is a direct assessment of the confidence level.
When comparing groups of respondents on a specific attribute level, then the Frequentist approach involves using the Zero-Centered Diffs utilities and running an F-test.
For Bayesian tests comparing groups of respondents, one typically uses HB's option of using the group variable as a covariate. The "alpha draws" now become more complicated in the output, but may be referenced for counting how many of the used draws show one group preferring that level over a different group.