any ideas on an introductory statistics book with a good deal of rigor?
Hmm I don't know about rigor. But they use this one at my school: The Practice of Statistics.
It's not that rigorous by the way.
Mathematical Statistics with Applications, 7th edition by Wackerley, Mendenhall, and Scheaffer
I know you asked for rigor, and I don't really know what any good books are for that. I used Mathematical Statistics with Applications by Wackerly/Mendenhall/Scheaffer in school, and it was a good book. Not great or bad.
A good introduction to statistics and probability is https://www.amazon.com/Head-First-Statistics-Dawn-Griffiths/dp/0596527586". Do not write this book off based upon its look of silliness (just look at its reviews). The Head First series are fantastic books (I learned Java and HTML from them). My girlfriend used this book to supplement a mathematical statistics course in her third year, so it obviously has some helpful material. It definitely isn't your standard textbook and it is best to read through it. I cannot recommend the Head First series enough, but I'm not for sure how much rigor (in terms of proofs?) you are wanting.
I'm not sure if the OP is looking for a mathematical statistics book. Reconciling introductory statistics with real mathematical rigor is not always clear. If I'm not mistaken, many mathematical statistics texts will presume familiarity with advanced calculus or mathematical analysis. Thus, if you've never really studied statistics before (beyond really basic stuff), you might want to look at something more basic than what has been prescribed. Of course, introductory statistics books are usually not mathematically rigorous in the sense that you probably won't see many proofs. But again, I think (though I am not sure) that more rigorous treatments require an appreciable amount of mathematical background.
Introduction to Mathematical Statistics by Hogg and Craig is what we used for our course on Probability and Statistics. But this was a course primarily aimed at application -- for engineers. So if you are looking for formal Probability Theory, you may not be satisfied with this book.
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