NEW YORK — President Donald Trump’s administration this week acknowledged it made a significant error in figures it used to help justify a fraud probe into New York’s Medicaid program, a glaring mistake that undercuts a federal campaign to tackle waste, mostly in Democratic-led states.

The error, one of at least a few misrepresentations in its description of the program, prompted health analysts to question how many of the Republican administration’s sweeping anti-fraud efforts around the country were based on faulty findings. It also reflected a common criticism that’s been made of Trump’s second administration — that it tends to attack first and confirm the facts later.

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