Teams in the National Football League (NFL) are given a ?bye? during 1 week of the season, when they can rest and not play a game. This may provide an advantage for the team in the next game they play after a bye.

In 2016, each of the 32 NFL teams was granted a bye during one of the weeks of the season. The following table contains the team name and the number of points they won by or lost by in the game after the bye (espn.com/nfl/, retrieved December 22, 2016). A positive value indicates that the team coming off the bye won the game, and a negative value means that they lost. Consider these results to be a representative sample from a population of possible NFL match-ups between teams where one of the teams is coming off a bye week.

a. Construct a graphical display for the data. Although the sample size is at least on the borderline of being adequate for t distribution methods, what characteristic of the distribution indicates that the methods based on the t distribution may not be appropriate?

b. Use a randomization test (Shiny app: ?Randomization Test for One Mean?) to perform a test of the hypothesis that the population mean points difference for NFL teams coming off a bye week differs from zero. Use a 0.05 significance level.

c. Use the results from Part (b) to explain whether or not teams coming off a bye week have a significant advantage in points scored over their opponents.

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Team Points Team Points ARI 3 LA -3 ATL 19 MIA 4 BAL MIN -11 BUF 4 NE -7 CAR 10 NO 3 CHI -26 NYG CIN -1 NYJ -5 CLE -13 OAK DAL PHI -1 DEN -3 PIT -7 DET SD GB SEA 2 HOU 3 SF - 18 IND TB 17 JAX TEN 3 KC 16 WSH