In the 2012 National Football League (NFL) season, the first three weeks’ games were played with replacement referees because of a labor dispute between the NFL and its regular referees. Many fans and players were concerned with the quality of the replacement referees’ performance. We could examine whether data might reveal any differences between the three weeks’ games played with replacement referees and the next three weeks’ games that were played with regular referees. For example, did games generally take less or more time to play with replacement referees than with regular referees? The pair of dotplots below display data about the duration of games (in minutes), separated by the type of referees officiating the game.

1. What proportion of the 47 games officiated by replacement referees lasted for at least 3.5 hours (210 minutes)? What proportion of the 42 games officiated by regular referees lasted for this long?

2. What proportion of the 47 games officiated by replacement referees lasted for less than 3 hours (180 minutes)? What proportion of the 42 games officiated by regular referees lasted for this long?

3. Would you say that either type of referee tended to have longer games than the other on average, and if so, which type of referee tended to have longer games and by about how much on average?

i. Regular Referees have longer game times with games about 185 minutes on average.

ii. The game lengths for both referees seem to be the same.

iii. Replacement Referees have longer game times with games about 195 minutes on average.

iv. It is too hard to tell from the graph which type of referee has longer games.

4. Would you say that either type of referee tended to have more variability in game durations? If so, which type of referee tended to have more variability?

i. The two types of referees had the same amount of variability in the game lengths.

ii. There is no way to tell which group of referees had more variability in the game lengths.

iii. The regular referees tended to have more variability in the game lengths.

iv. The replacement referees tended to have more variability in the game lengths.

For replacement total games = 47 more than 3.5 hours = 8 required proportion = 8/47 = 0.170212 for regular.