Question: A common quandary faces sports fans who live in the same city but avidly follow different sports. How does one determine whose team did better with respect to its league division? In 2004, the Boston Red Sox won the World Series; just months later, their local football counterparts, the New England Patriots, won the Super Bowl. In 2005, both teams made the play-offs but lost early on. Which team was better in 2005? The question, then, is: Were the Red Sox better, as compared to other teams in the American League of Major League Baseball, than the Patriots, as compared to the other teams in the American Football Conference of the National Football League? Some of us could debate it for hours, but it's better to examine some statistics. Let's operationalize performance over the season as the number of wins during regular season play.
a. In 2005, the mean number of wins for baseball teams in the American League was 81.71, with a standard deviation of 13.07. Because all teams were included, these are population parameters. The Red Sox won 95 games. What is their z score?
b. In 2005, the mean number of wins for football teams in the American Football Conference was 8.13, with a standard deviation of 3.70. The Patriots won 10 games. What is their z score?
c. Which team did better, according to these data?
d. How many games would the team with the lower z score have had to win to beat the team with the higher z score?
e. List at least one other way we could have operationalized the outcome variable (i.e., team performance).