Final answer:
Official government websites and reputable institutions like the U.S. Department of Homeland Security, the United States Census Bureau, and the Migration Policy Institute are credible sources for U.S. immigration statistics.
Step-by-step explanation:
A credible website for statistics about modern U.S. immigration would include official government sources such as the U.S. Department of Homeland Security's Office of Immigration Statistics. Their publications, such as the "Yearbook of Immigration Statistics," offer comprehensive data on immigration. Additional trustworthy sources are the Bureau of Labor Statistics and the United States Census Bureau, which both provide extensive statistics on various aspects including immigration. The Migration Policy Institute is another reputable source with frequently requested statistics on immigrants and immigration in the United States. When considering non-governmental sources, look for reputed research institutions or nonpartisan organizations like ProCon.org, which explores various solutions to illegal immigration in America.