Which of the following statements is true about Kappa Alpha Psi?

The statement that Kappa Alpha Psi was established in the 20th century is accurate because the fraternity was founded on January 5, 1911, at Indiana University. This time period places it squarely in the early part of the 20th century, aligning with the founding of several other Black Greek-letter organizations during a time of great development for African American collegiate communities.

The other statements are not accurate; the fraternity was specifically founded by African American male students, rather than women, and it has official colors of crimson and cream. Additionally, Kappa Alpha Psi is indeed recognized by the National Pan-Hellenic Council, which is the umbrella organization for historically African American fraternities and sororities.