In the 2012 National Football League (NFL) season, the first three weeks’ games
ID: 3180843 • Letter: I
Question
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. The pair of dotplots shown display data on the total number of penalties called in the game, again separated by the type of referee. Select all the statements below which might reveal whether the two types of referees differ with regard to the distributions of this variable.
1) Both distributions are fairly symmetric, centered around 12 penalties, with a minimum of 4 penalties and a maximum of 24-25 penalties.2) The number of penalties assessed by regular referees seems to be higher than the number of penalties assessed by replacement referees.
3) The games with 23-25 penalties are a bit unusual for both types of referees, with a few more of these extreme games for the replacement referees.
4) The game that had the highest number of penalties assessed was officiated by a regular referee. Regular Replacement 12 15 Total penalties 18 21 24
Explanation / Answer
We will check each and every statement in this case
the first statements tells us that both distributions are symmetric nd centerec around 12 penealties, with a minimum 4 penalties and maximum 24 - 25 penalties so this statement, first it is wrong in the case of symmetric around 12 and second it doesn't tell about the differences between two distributions
The second statement "The number of penalties assessed by regular referees seems to be higher than the number of penalties assessed by replacement referees" The second point is also wrong as the number of penalties assessded by regular referees ( 544) and by replacement referees is ( 650 ) and this thing is not taking avrage into consideration as number of matches referred by replacement referees is more than regular refrees.
the statement "The games with 23-25 penalties are a bit unusual for both types of referees, with a few more of these extreme games for the replacement referees." Yes this can be a valid point to show the difference that both distribution differ. Here the extreme values are higher in case of replacement refrees that shows a high variance distribution with respect to regular referres.
The point 4 is "The game that had the highest number of penalties assessed was officiated by a regular referee." but it doesn't show anything unique or unusual about the distributions of both type of referees so it is a true statement but not a valid statement.