Final answer:
American businesspeople were concerned about the political situation in Cuba in the late 1800s due to the fear that Spain's loss of control would lead to instability, which would affect their economic interests and the United States' strategic interests in the region.
Step-by-step explanation:
Many American businesspeople were nervous about the political situation in Cuba in the late 1800s chiefly because they feared that Spain would lose control of Cuba, leading to instability. This concern was rooted in several factors, including the strategic significance of Cuba, its proximity to the United States, and the economic interests Americans had in the island.
From the early efforts to purchase Cuba to the Monroe Doctrine's assertion of American interest in the Western Hemisphere, it's apparent that Americans had longstanding interests in the region. The late 19th century was marked by the Cuban struggle for independence, which culminated in the Spanish-American War, further intertwining the fates of the United States, Cuba, and Spain.