In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 250 of these people said they never did so

(“Rebates: Get What You Deserve,” Consumer Reports, May 2009: 7). Reasons cited for their behavior included too many steps in the process, amount too small, missed deadline, fear of being placed on a mailing list, lost receipt, and doubts about receiving the money. Calculate an upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate.

Based on this bound, is there compelling evidence that the true proportion of such consumers is smaller than 1/3?

Explain your reasoning.