Final answer:
The United States sought a sphere of influence in China to compete economically and strategically in the region during a time when Western powers and Japan were carving up China for trade and investment. The U.S. advocated for the Open Door Policy, which aimed to ensure equal commercial opportunities for all nations in China and prevent exclusive control by any single power.
Step-by-step explanation:
The United States' desire for a sphere of influence in China during the late 19th and early 20th centuries was rooted in economic and strategic interests. The historical context of the time shows that as China was weakened by internal strife and external pressures, Western powers and Japan were establishing spheres to secure trade and investment opportunities. The Open Door Policy proposed by the U.S. was a strategy to ensure that it could compete on equal footing in China without having its own exclusive sphere. This policy was partly an assertion that the U.S. was there to stay in the region, emphasizing equal commercial opportunities for all nations in China, countering the exclusive control other powers sought. The U.S. believed that this policy was fair as it prevented colonization and preserved China's territorial integrity while still allowing American businesses to access the Chinese market.