Test of Two Variances · Exercise 25

The American League and the National League of Major League Baseball are each divided into three divisions: East, Central, and West. Many years, fans talk about some divisions being stronger (having better teams) than other divisions. This may have consequences for the postseason. For instance, in a certain year Tampa Bay won 90 games and did not play in the postseason, while Detroit won only 88 and did play in the postseason. This may have been an oddity, but is there good evidence that in this year, the American League divisions were significantly different in overall records? Use the following data to test whether the mean number of wins per team in the three American League divisions were the same or not. Note that the data are not balanced, as two divisions had five teams, while one had only four.

$$\begin{array}{ccc}\text{Division}& \text{Team}& \text{Wins}\\ \text{East}& \text{NY Yankees}& \text{95}\\ \text{East}& \text{Baltimore}& \text{93}\\ \text{East}& \text{Tampa Bay}& \text{90}\\ \text{East}& \text{Toronto}& \text{73}\\ \text{East}& \text{Boston}& \text{69}\end{array}$$

$$\begin{array}{ccc}\text{Division}& \text{Team}& \text{Wins}\\ \text{Central}& \text{Detroit}& \text{88}\\ \text{Central}& \text{Chicago Sox}& \text{85}\\ \text{Central}& \text{Kansas City}& \text{72}\\ \text{Central}& \text{Cleveland}& \text{68}\\ \text{Central}& \text{Minnesota}& \text{66}\end{array}$$

$$\begin{array}{ccc}\text{Division}& \text{Team}& \text{Wins}\\ \text{West}& \text{Oakland}& \text{94}\\ \text{West}& \text{Texas}& \text{93}\\ \text{West}& \text{LA Angels}& \text{89}\\ \text{West}& \text{Seattle}& \text{75}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §13.4 Test of Two Variances · Exercise 25