Question

The New England Patriots. The 2017 roster of the New England Patriots, winners of the 2017 NFL Super Bowl included 12 defensive linemen and 9 offensive linemen. The Minitab Express file for this problem contains the weights in pounds of the offensive and defensive linemen. Use this data set to test the claim that the defensive linesmen weigh less that the offensive linemen at the 5% level of significance.

Number   Name   Position   Weight   Line
97   Branch, Alan   NT   325   Defensive Line
99   Buchanan, Michael   DE   255   Defensive Line
74   Easley, Dominique   DE   290   Defensive Line
98   Forston, Marcus   DT   305   Defensive Line
95   Jones, Chandler   DE   265   Defensive Line
94   Jones, Chris   DT   309   Defensive Line
90   Moore, Zach   DE   275   Defensive Line
50   Ninkovich, Rob   DE   260   Defensive Line
96   Siliga, Sealver   DT   325   Defensive Line
90   Smith, Will   DE   282   Defensive Line
72   Vellano, Joe   DT   300   Defensive Line
75   Wilfork, Vince   DT   325   Defensive Line
61   Cannon, Marcus   G   335   Offensive Line
63   Connolly, Dan   G   305   Offensive Line
65   Devey, Jordan   G   317   Offensive Line
71   Fleming, Cameron   G   325   Offensive Line
67   Kline, Josh   G   295   Offensive Line
77   Solder, Nate   T   320   Offensive Line
66   Stork, Bryan   C   310   Offensive Line
76   Vollmer, Sebastian   T   320   Offensive Line
62   Wendell, Ryan   G   300   Offensive Line

Answer 1

The test statistic and critical point has been found by running the following R code:

off <- c(335,305,317,325,295,320,310,320,300)
def <-c(325,255,290,305,265,309,275,260,325,282,300,325)
t.test(off,def,alternative="greater",var.equal=TRUE)
qt(0.95,19)