  Recently we proposed quantum language(or, measurement theory), which is
characterized as the linguistic turn of the Copenhagen interpretation of
quantum mechanics. Also, we consider that this is a kind of system theory such
that it is applicable to both classical and quantum systems. As far as
classical systems, it should be noted that quantum language is similar to
statistics. In this paper, we discuss the usual confidence interval methods in
terms of quantum language. And we assert that three concepts (i.e.,"estimator"
and "quantity" and "semi-distance)are indispensable for the theoretical
understanding of the confidence interval methods. Since our argument is quite
elementary, we hope that the readers acquire a new viewpoint of statistics, and
agree that our proposal is, from the pure theoretical point of view, the true
confidence interval methods.
  (Key words: Confidence interval, Chi-squared distribution, Student's
t-distribution)
