Question

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 188 bids by​ super-experienced bidders, 25 winning bids were above the​ item's expected​ value, and of the bids by the 140 less-experienced bidders, 31 winning bids were above the​ item's expected value.

Construct a 90% confidence interval for (p1 - p2).

( _________, _________ ).

(Round to three decimal place as needed).

Answer 1

Solution :

Given that,

n₁ = 188

x₁ = 25

₁ = x₁ / n₁ = 0.133

n₂ =140

x₂ = 31

₂ = x₂ / n₂ = 0.221

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.133 - 0.221

= -0.088

2)

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

= 1.645 (use z table)

Margin of error =   *

=  

=

= 0.0705

3) Required interval is

Point estimate   Margin of error

-0.088   0.0705

(-0.088 - 0.0705 , -0.088+  0.0705)

(-0.159 , -0.018)