How might a person who agreed with Hoover respond to Woodward’s claim that work relief programs are improving communities?

That person would most likely rejected the claim.

Explanation:

President Hoover was known for his stance to support limited government. He believed that the economy should be run through the power of market competition and the government should give as little as intervention as possible.

This made him believe that relief programs offered to the poor is a form of 'handouts' that only make people becomes lazy. He believed this will negatively impacted the economy.

Because of this, People who agreed with this view would most likely reject the claim that work relief programs are improving communities.