Here are four sports problems, and three of them are based on true stories! Identify which problems call for a t-test, which call for a regression analysis, and which are handled by neither. So the choices for filling in the blanks are t-test, regression, and neither. (Obviously one answer will need to be used twice.)

a) A quarterback (Tom) was accused of using deflated footballs, which are easier to throw and catch, in key games. A football is supposed to be inflated to between 12.5 and 13.5 pounds per square inch. Of course, there is some variation in how inflated the balls are

(yes, folks, that variation is the SD), so it is quite possible that, every once in a while, the footballs Tom used might be a bit underinflated. The inflation level of a set of balls that Tom used in key games was tested, and the mean inflation for those balls was computed and recorded along with the SD. This mean was then compared to the mean level of inflation of balls used by all quarterbacks in the league over the whole season to see if the footballs Tom used were significantly different.

b) A major league baseball team was accused of cheating in its home games in 2017.

Allegedly, it observed the opposing catchers’ signals and then communicated these to the team’s batters (“sign stealing”). Although teams often have a higher batting average at home than away, a large difference between the team’s home and away batting averages could be interpreted as a sign that cheating was taking place during home games. (A batting average is actually a proportion, computed as the number of hits divided by the number of at bats. It is expressed as a decimal fraction, computed to three places. What proportion of at bats resulted in a hit?) Were the team’s home and away batting averages unusually different?

c) Is bat speed related to how far a ball flies when it is hit? We examine this relationship by having 200 balls hit by bats that all have the same weight (“controlling for bat weight”), measuring bat speed with a small device attached to the bats, and then measuring the distance the balls flew.

d) Do fans at National League (NL), American League (AL), and Minor League (MiLB)

ballparks have similar taste in ballpark food? There are four categories of food: hot dogs, pizza, nachos, and other. We asked fans in each category of ballpark (NL, AL, and MiLB)

to identify their favorite type of ballpark food.