I am learning Statistics and I encounter the problems of how people come up with the test statistics for each testing method, what methods to choose, the strength and weakness of each method as well as the graphical representation of the distributions under $H_0$ and $H_1$. I would like to learn and read it in a detailed and comprehensive textbook so that I can have a clear and solid understandings and intuitions about hypothesis testing. Could anyone please give me some recommendations?
Thank you so much for your help!
The first book I read for this was one called An Introduction to Probability and Statistics for Engineers and Scientists, by Sheldon Ross. There are better books for introductory probability but I find this to be a nice book for the sections you’re interested in. There are many books by this chap, so make sure you pick the right one.
In case you don’t like it, you might consider looking up lecture notes; this is by no means a very niche subject, so I expect there to be a lot of resources on this. They often do a better job than traditional, verbose texts.
Also, a little more about your background would make it easier for people to give suitable recommendations.