We evaluate the model averaged profile likelihood confidence intervals
proposed by Fletcher and Turek (2011) in a simple situation in which there are
two linear regression models over which we average. We obtain exact expressions
for the coverage and the scaled expected length of the intervals and use these
to compute these quantities in particular situations. We show that the
Fletcher-Turek confidence intervals can have coverage well below the nominal
coverage and expected length greater than that of the standard confidence
interval with coverage equal to the same minimum coverage. In these situations,
the Fletcher-Turek confidence intervals are unfortunately not better than the
standard confidence interval used after model selection but ignoring the model
selection process
