What is the name for the Muslims who live in northwestern China?

The correct choice is Uighurs, which refers to a specific ethnic group of Muslims primarily found in the Xinjiang Uighur Autonomous Region of northwestern China. The Uighurs have a distinct culture, language, and history that sets them apart from other groups within China. Historically, they have been known for their significant contributions to trade along the Silk Road and for maintaining their unique cultural and religious identity despite regional pressures and political developments.

The other options refer to different groups or terms within the context of China. Tibetans are an ethnic group mainly residing in Tibet, and they practice Tibetan Buddhism, which is different from the Islamic faith of the Uighurs. Mandarin is a term that primarily refers to the standard Chinese language, not an ethnic group. Falun Gong is a spiritual movement combining meditation and qigong exercises, and it is not an ethnic group, but rather a practice that has been suppressed by the Chinese government. Thus, identifying Uighurs as the correct answer emphasizes their distinct cultural, religious, and geographical significance within China.