  A distributed binary hypothesis testing (HT) problem over a noisy (discrete
and memoryless) channel studied previously by the authors is investigated from
the perspective of the strong converse property. It was shown by Ahlswede and
Csisz\'{a}r that a strong converse holds in the above setting when the channel
is rate-limited and noiseless. Motivated by this observation, we show that the
strong converse continues to hold in the noisy channel setting for a special
case of HT known as testing against independence (TAI). The proof utilizes the
blowing up lemma and the recent change of measure technique of Tyagi and
Watanabe as the key tools.
