In auction bid-ding, the "winner's curse" is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. 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 value; in the less-experienced group, 32 of 149 winning bids were above the item's expected value.
a. Find an estimate of p, the true proportion of super-experienced bidders who fell prey to the winner's curse.
b. Find an estimate of p2, the true proportion of less-experienced bidders who fell 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.