Can I be added too? (I have yet to finish my master degree, but what should have been my master thesis transformed in three papers and I want to continue...)

A far wiser man said that asking if they are reasoning is like asking if submarines swim, furthermore probably for somebody the concept of "reasoning" is too much linked with some animistic assumption about the process that lead to our thinking

Lehmann's "Testing Statistical Hypotheses" is surely comprehensive however might be a little advance, Barlow's "Statistics: A guide to the use of statistical methods..." was one of the most used by undergrad physicists to introduce them to the theory of errors, fitting data and so on