god i hate being the bad guy, ONE THIS IS A TRIVIA SECTION NOT A HOMEWORK HELP SECTION, TWO DO YOUR OWN WORK AND STOP ASKING OTHERS TO DO YOUR PROJECT. god i hate doing that. mmmmmmmmmmmm.... pie.....
A conspiracy simply means two or more people discuss and agree to do something. Since 4 aircraft were commandeered by 19 men it seems obvious to me that a conspiracy existed.
I think the answer to the unasked portion of your question is NO; I don't believe nor is there any evidence to indicate the President or any covert or over American agency were responsible for or had advanced warning of the specifics of the attack.