"Defense wins championships" is a common phrase used in the National Football League. Is defense associated with winning? The following data represent the winning percentage and the yards per game allowed during the 2014-2015 season for a random sample of teams.

(a) Test the belief that defense wins championships by determining whether a higher winning percentage is associated with a lower number of total yards given up at the α = 0.10 level of significance.
(b) Draw a scatter diagram to support your conclusion.

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Team Winning Percentage Total Yards Baltimore Ravens 0.625 336.9 Cleveland Browns 0.438 366.1 Denver Broncos 0.750 305.2 Jacksonville Jaguars 0.188 370.8 0.750 New England Patriots 344.1 Oakland Raiders 357.6 0.188 Pittsburgh Steelers 0.688 353.4