Which of these is not an Ivy League University?

Stanford is not an Ivy League University.

The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term Ivy League has connotations of academic excellence, selectivity in admissions, and social elitism.

While the term was in use as early as 1933, it became official only after the formation of the NCAA Division I athletic conference in 1954. Seven of the eight schools were founded during the United States colonial period; Cornell was founded in 1865. Ivy League institutions account for seven of the nine Colonial Colleges chartered before the American Revolution; the other two are Rutgers University and the College of William & Mary.