In sealed bidding on state road construction contracts, the “winner’s curse” is the phenomenon of the winning (or highest) bid price being above the expected price of the contract (called the Department of Transportation engineer’s estimate). The Review of Economics and Statistics (Aug. 2001) published a study on whether bid experience impacts the likelihood of the winner’s curse occurring. Two groups of bidders in a sealed-bid auction were compared: (1) super-experienced bidders and (2) less-experienced bidders. In the super-experienced group, 29 of 189 winning bids were above the item’s expected price; in the less-experienced group, 32 of 149 winning bids were above the item’s expected price.

a. Find an estimate of p₁, the true proportion of super experienced bidders who fall prey to the winner’s curse.

b. Find an estimate of p₂, the true proportion of less experienced bidders who fall prey to the winner’s curse.

c. Construct a 90% confidence interval for p₁ - p₂.

d. Give a practical interpretation of the confidence interval, part c. Make a statement about whether bid experience impacts the likelihood of the winner’s curse occurring.