To accurately determine which belief the image reflects, I would need more context regarding the content of the image in question. However, based on the options provided, the belief that "The United States was responsible for protecting Latin America from European interference and colonization" aligns well with the sentiments expressed in the Monroe Doctrine and Roosevelt Corollary, which were prevalent early in the twentieth century.
If the image suggests themes of American intervention or protection in Latin America, that would be the most direct connection to popular beliefs of that era.
If the image were to depict naval power or military strength, then "The United States needed to increase the size of its Navy to become a legitimate world power" could also be a fitting response.
Please provide additional details about the image for a more precise interpretation.