I have an upcoming statistics exam and I'm studying it on my own. I was recommended Hogg's Introduction to Mathematical Statistics, but I didn't find it helpful. I just want a book which covers basic mathematical statistics and statistical inference: stochastic convergence, estimation of parameters, testing hypothesis, etc. all at an elementary level (suitable for a math undergraduate), with good introduction to the required background for such concepts. Can you provide me a good source?
My favorite undergraduate statistics textbook is the textbook "All of statistics" by Larry Wasserman. In particular it is great for acquiring statistical intuition. The flow throughout the text is very coherent, i.e. you really get the sense of how all the different methods come together and form a statistician's toolbox. In contrast, I find that in many other introductory textbooks reading through them feels like plowing through an assortment of random topics, often cookbook recipes even.
Regarding the material, it covers all the basics, as enumerated in your post. This corresponds to approximately 200 pages of the book. The rest covers more advanced topics (yet the presentation remains at the same elementary level as before), such as causality, probabilistic graphical models and kernel density estimation, which are often omitted from introductory books.
One caveat is that I read the book once I already knew the content, so it might be too concise for a first reading. In the preface the author mentions that it is suitable for advanced undergraduates.
Another book which is often recommended (and included in the Syllabus of such courses) is the book "Mathematical Statistics and Data Analysis" by John Rice. I personally did not like this book though, it felt too verbose, but you could also take a look into that.