Final answer:
Roosevelt's involvement in the 1902 Anthracite Coal Strike marked the first time a president directly intervened as a mediator in a labor dispute and set a new precedent for federal intervention in strikes that threatened public welfare.
Step-by-step explanation:
The "firsts" attributed to Roosevelt for his involvement in the coal miners' strike include his direct intervention as a mediator in the labor dispute. During the 1902 Anthracite Coal Strike, President Theodore Roosevelt demonstrated a new precedent whereby the federal government would expect to intervene when a strike threatened public welfare.
Roosevelt invited both sides to the White House for negotiations and threatened to use the military not to break the strike but to operate the mines if a compromise couldn't be reached, which was a progressive move at that time. Eventually, the miners received a 10 percent raise, but their demand for only union labor was not met, representing a compromise between labor's requests and management's stance.