Final answer:
The data does not explicitly identify which president had the greatest influence on the federal judiciary. Two-term presidents have made over three hundred judicial appointments, impacting the judiciary's composition based on their own ideological preferences.
Step-by-step explanation:
The president with the greatest influence on the composition of the federal judiciary, as measured by the percentage of judgeships filled, is not explicitly clear from the available data. However, it is known that two-term presidents have nominated well over three hundred federal judges while in office. This significant number demonstrates the president's lasting impact on the judiciary system, emphasizing the importance of the advice and consent process of Congress in confirming these lifetime appointments.
Presidents Ronald Reagan, George W. Bush, Bill Clinton, and Jimmy Carter all served at least one full term, providing opportunities to nominate federal judges, including Supreme Court justices. Their influence on the judiciary, to some extent, reflects their own ideological leanings, as judicial appointments serve for life. For example, Reagan's presidency was noted for controversial Supreme Court nominees, while George W. Bush appointed significant conservative figures like Samuel Alito, who remains on the court.