Question

3.52 Super Bowl Problem 3.8 shows the difference in total yards between the winner and loser of the Super Bowl. On average, the winning team gained 75.98 yards more than the losing team with standard deviation 111.03 yards. Super Bowl XLIV was won by New Orleans over Indianapolis, even though New Orleans had 100 fewer yards than Indianapolis.

(a) What is the data value for Super Bowl XLIV between New Orleans and Indianapolis?

(b) Find the standardized score.

(c) Interpret what the standardized score tells you about the yardage difference in Super Bowl XLIV.

Answer 1

The number of yards winning team gained over the losing team is

New Orleans had 100 fewer yards than Indianapolis.

That is the number of yards winning New Orleans gained over the losing team Indianapolis is (- 100)

a) Hence the data value for Super Bowl XLIV between New Orleans and Indianapolis is (- 100)

b) Standardized score is

c) the standardized score tells us about that the yardage difference in Super Bowl XLIV that New Orleans had 1.5850 Standard deviations less Yard scored than New Orleans