In auction bidding, the "winner's curse" is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. A study was conducted to see if less-experienced bidders were more likely to be impacted by the curse than super-experienced bidders. The study showed that of the 185 bids by super-experienced bidders, 26 winning bids were above the item's expected value, and of the bids by the 138 less-experienced bidders, 37 winning bids were above the item's expected value. Complete parts a through d.
a. Find an estimate of p1, the true proportion of super-experienced bidders who fall prey to the winner's curse.
p1 = .141
b. Find an estimate of p2, the true proportion of less-experienced bidders who fall prey to the winner's curse.
p2 = .268
c. Construct a 90% confidence interval for (p1 - p2).