Final answer:
The claim that Show Boat established the true American musical in the late 1920s, combining story, music, and dance, is true and set forth a new era in musical theatre.
Step-by-step explanation:
The statement that the true American musical, combining music, dance, and a singular dramatic story at the center, was first established in the late 1920s with the musical Show Boat, is true. Jerome Kern and Oscar Hammerstein's Show Boat, which debuted in 1927, revolutionized musical theatre by incorporating a more complex and dramatic story that included serious social issues. It was an evolutionary step that combined all the best elements of structure, song formulas, and character development from previous shows, which paved the way for the Golden Age of Musical Theatre. This era saw masterpieces like Oklahoma! and Guys and Dolls, which maintained this tradition of rich storytelling combined with music and dance.