= Solution
<Lepton universality> means that the weak <charged current> couples equally to the three charged <lepton> families after accounting for <masses> and known radiative corrections. In the ratio of two <tau lepton> <leptonic decay> widths, the parent <coupling constant (physics)>, <mean lifetime> and $m_\tau^5$ cancel:
$$
\frac{B_\mu}{B_e}=\frac{|g_\mu|^2}{|g_e|^2}\frac{f_{\tau\mu}}{f_{\tau e}}.
$$
The universal prediction is $B_\mu/B_e=0.97256/0.9999993=0.9725607$. The measured ratio is $17.41/17.83=0.97644$, giving
$$
\boxed{\frac{|g_\mu|}{|g_e|}=1.00199\pm0.00161}
$$
if the quoted errors are treated as independent. This is consistent with unity at about $1.2$ standard deviations. An actual precision fit must retain the measured covariance and the small radiative corrections; the rounded table alone does not supply those correlations.
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