Final answer:
During the 1960s and '70s, noncontributory public assistance programs expanded significantly with the establishment of Medicare in 1965 as a part of President Lyndon B. Johnson's 'Great Society' campaign.
Step-by-step explanation:
Like contributory programs, the noncontributory public assistance programs also made their most significant expansion during the 1960s and '70s. The largest single category of expansion was the establishment in 1965 of Medicare.
During this time under President Lyndon B. Johnson, the administration passed the Social Security Act of 1965, which was a significant overhaul to the welfare state and resulted in the creation of Medicare, a federal program designed to provide healthcare to the elderly. The creation of these programs, along with Medicaid and other social welfare programs, were central to Johnson's "Great Society" initiative aimed to eliminate poverty by expanding federal support for health, education, and welfare services.