A Generalized Confidence Interval approach to comparing log-normal means, with application

Generalized Confidence Intervals (GCI) can be constructed for cases where an exact confidence interval based on sufficient statistics is not available. In this thesis, we first review three existing tests for log-normal data using the GCI approach. Then we propose fiducial generalized pivotal quantities (FGPQ)-based simultaneous confidence intervals for ratios of log-normal means, and prove that the constructed confidence intervals have correct asymptotic coverage. These methods are then applied to a dataset from the Carbon Reduction Commitment Energy Efficiency Scheme (CRC) to test for differences between energy saving percentages among different groups.