Absolutely. So wouldn't it be neat if premedical students and business majors had already seen a thorough stats class in high school, so that their college-level stats classes could spend less time on the basics and more time on those subtleties?
(Speaking as someone who's taught calculus-based physics to premedical students, I think it's important to recognize that most folks who've taken a year of calculus really have not internalized those concepts enough to be fluent in applying them. I think it would take a particularly strong math background for someone to really understand the mathematical justifications for statistics, so I suspect class time would be better spent warning students about pitfalls than on hoping that they will draw meaningful conclusions from formal derivations. Heck, medical students are required to have taken calculus, but lots of them (evidently including a journal editor, peer reviewers, and 163 followup papers) apparently don't even know what an integral is: http://fliptomato.wordpress.com/2007/03/19/medical-researche... .)
(Speaking as someone who's taught calculus-based physics to premedical students, I think it's important to recognize that most folks who've taken a year of calculus really have not internalized those concepts enough to be fluent in applying them. I think it would take a particularly strong math background for someone to really understand the mathematical justifications for statistics, so I suspect class time would be better spent warning students about pitfalls than on hoping that they will draw meaningful conclusions from formal derivations. Heck, medical students are required to have taken calculus, but lots of them (evidently including a journal editor, peer reviewers, and 163 followup papers) apparently don't even know what an integral is: http://fliptomato.wordpress.com/2007/03/19/medical-researche... .)