Yes. The U.S. Census Bureau is bound by law to protect your answers and keep them strictly confidential. In fact, every employee takes an oath to protect your personal information for life.
The Census Bureau is bound by Title 13 of the U.S. Code to keep your information confidential.The answers you provide are used only to produce statistics. You are kept anonymous: The Census Bureau is not permitted to publicly release your responses in any way that could identify you or anyone else in your home.