Does intended major/school matter?

Throughout high school I have been set on majoring in some sort of business field, and have many ECs that show my strength (business competitions, manager of ~7 employees at work, designed a marketing plan for a new product line at a local business, stuff like that). However, when actually deciding between colleges and majors, industrial engineering seems to be what I am most interested in. I have a decently strong math background, (Calc BC as junior, going to take two courses at local college next year) but no ECs related to math or engineering of any kind. Also haven’t challenged myself in science at all. Would applying as a business major give me a better chance at getting into the university? Also, how difficult is it to switch schools after you get accepted (business to engineering). Planning on applying to places like Northwestern, Penn, Michigan, USC.

(Yes, I am aware that I should just apply to what I am truly passionate about and not think about what will give me a better chance of getting into the college, but I am curious if anyone has any experiences they can share)

http://talk.qa.collegeconfidential.com/college-admissions/1947599-faq-does-intended-major-make-it-easier-or-more-difficult-to-get-into-a-college.html

If you actually prefer IE, specify IE as your major.

For Michigan, Ross is as competitive as CoE, if not more. They also have different freshmen requirement. In addition, any school specific merit aid would not be transferable. Nevertheless, transferring from LSA to CoE is relatively easy and the admission to LSA is slightly easier.

Thanks, I figured there was some thread about this but I was unable to find it. And it’s not just if applying to a different school would give me a better chance, but I have specific achievements/ECs that show my dedication and success in business that would seem to really strengthen my application, but I’m assuming they wouldn’t help me at all if I applied as engineering.