For years I have recommended the textbooks authored or co-authored by David Moore as high quality. However, a couple of months ago, I started hearing complaints about Introduction to the Practice of Statistics, which my department has been using for its undergraduate Applied Statistics course for math majors. It seems that some topics have been omitted, many challenge problems dropped, and some of the writing is of poorer quality than in previous editions. (Note: Moore, although still listed as co-author, no longer is involved in revising the book.) So I volunteered to look for a more suitable text.
The best one I’ve found is Stats: Data and Models, 3rd edition by De Veaux, Velleman and Bock (Pearson, 2012). It is in many ways in the tradition of Moore’s book, emphasizing the importance of model assumptions. In addition, it has more of the math, which is desirable for the course in question. The writing style is lively, and the organization seems well-thought out. (Note: The same trio of authors also have two other books, Intro Stats, which omits much of the math and is appropriate for an intro course for students in non-STEM fields, and Stats:Modeling the World, with Bock as first author, intended for the AP statistics audience.)
One that I definitely do not recommend is Kokoska, Introductory Statistics: A Problem-Solving Approach (Freeman, 2011). The author is well-intended, but misguided. Well-intended: He has identified a few areas where students have difficulty with what he is trying to teach, and has tried to point those out and guide the student past the difficulties. Misguided: Unfortunately, what he is trying to teach might be called “pseudo-statistics” or perhaps “applying statistical theory to a fantasy world.” He misses a lot of the important points in using statistics in the real world. For example, in many exercises labeled “applied,” he says, “assume the underlying distribution is normal.” In fact, his approach is largely cookbook; there is nothing really aimed at making the student an informed consumer of statistics, and a lot that could lead to misuses of statistics. (Example: Section 10.5 consists of several pages on the F-test for equal variances and the related confidence interval for the ratio of the two variances. On p. 500, he says that the test is often used to compare two population variances to decide whether or not the equal variance t-test is appropriate to compare the corresponding means. But he does not mention that this F-test is very sensitive to violations of model assumptions, and in fact is especially likely to be useless in exactly the situation of small sample sizes where it would be most desirable to be able to use the equal variance t-test for comparing means.) This is definitely not a suitable textbook for any intro stat course.
A third text is interesting: Rossman and Chance’s Investigating Statistical Concepts, Applications, and Methods. I have contacted several people who have used it, and my impression is: It is worth trying, if you have experience teaching in an investigative style, and have experience with permutation tests, and can use a classroom with computers for student use. Otherwise, expect a real challenge in using it.