  The Standard Model fit prefers values of the Higgs boson mass that are below
the 114 GeV direct lower limit from LEP II. The discrepancy is acute if the 3.2
sigma disagreement for the effective weak interaction mixing angle from the two
most precise measurements is attributed to underestimated systematic error. In
that case the data suggests new physics to raise the predicted value of the
Higgs mass. One of the simplest possibilities is a Z' boson, which would
generically increase the prediction for the Higgs mass as a result of Z-Z'
mixing. We explore the effect of Z-Z' mixing on the Higgs mass prediction,
using both the full data set and the reduced data set that omits the hadronic
asymmetry measurements of the weak mixing angle, which are more likely than the
leptonic asymmetry measurements to have underestimated systematic uncertainty.
