  We study the detection capability of the weak-value amplification on the
basis of the statistical hypothesis testing. We propose a reasonable testing
method in the physical and statistical senses to find that the weak measurement
with the large weak value has the advantage to increase the detection power and
to reduce the possibility of missing the presence of interaction. We enhance
the physical understanding of the weak value and mathematically establish the
significance of the weak-value amplification. Our present work overcomes the
critical dilemma of the weak-value amplification that the larger the
amplification is, the smaller the number of data becomes, because the
statistical hypothesis testing works even for a small number of data. This is
contrasted with the parameter estimation by the weak-value amplification in the
literature which requires a large number of data.
