Sports and Leisure Many hockey players use a slapshot-a short, quick, powerful swing with the stick-to try and score a goal. The speed of this shot makes it very difficult for a goalie to react and make a save. The fastest slapshot recorded was 108.8 mph in 2012 by Zdeno Chara.20 A National Hockey League (NHL) scout believes that defensemen have faster slapshots than forwards. To test this claim, independent random samples from each group of players were obtained. Each player took a slapshot from the blue line, and the speed of the puck was recorded (in mph) using a radar gun. The data are given in the following table.
Use the Wilcoxon rank-sum test with a = 0.01 to determine whether there is any evidence to suggest that the population median slapshot speed of NHL defensemen is greater than the population median slapshot speed of NHL forwards. Assume the underlying distributions are continuous.