Baseball fans who watch games on television can usually see something called the pitch tracker. It allows viewers to see whether the umpire made the correct call. According to rule 2.00 of the Major League Baseball rule book, a strike zone is defined as “that area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the kneecap” and is determined by “the batter’s stance as the batter is prepared to swing at a pitched ball.” 

For many fans, it appears that some umpires have bigger strike zones than others. That is, they call pitches strikes when the pitch was actually not in the strike zone. Umpires with large strike zones are likely to see less runs scored since the batter is at a disadvantage. We‘ll call this the Unequal Strike Zone Theory, which states that some umpires routinely enlarge the strike zone resulting in lower scores. Fortunately, this theory is testable. For every game in the 2015 season, the home plate umpire, the visiting team scores, the home team scores, and the total number of runs were recorded. Test the Unequal Strike Zone Theory. Conduct an analysis that determines whether there is sufficient evidence to infer that the total number of runs per game differs between the 91 home plate umpires?

*The author wishes to thank Mr. Stacey Albom for collecting all the data in this case.