. Baseball has always been a favorite pastime in America, and is rife with statistics and theories. While baseball purists may disagree, to an applied statistician no topic in baseball is too small or hypothesis too unlikely. In a recent paper, researchers at Wayne State University showed that major-league players who have nicknames live longer than those without them (The Wall Street Journal, July 16, 2009). You do not believe in this result and decide to conduct a test. Consider the following data on the lifespan of a player and the nickname variable, which equals 1 if the player had a nickname and 0 otherwise. (25 points)

Years

74

62

67

73

49

62

56

63

80

65

61

64

70

71

69

56

68

70

79

67

68

68

64

63

68

68

74

64

Nickname

1

1

1

1

1

0

0

0

1

1

0

0

0

1

1

0

1

1

1

0

1

0

1

1

0

1

1

1

0

0

a. Using the 5% level of significance, determine if the variances in lifespan differ between players with nicknames and players without nicknames. Follow and show the 7 steps for hypothesis testing. (8 points)

b. Use the 5% level of significance. Using the results found in part (a), perform a hypothesis test to determine if the average lifespan differs between players with nicknames compared to those without nicknames. Follow and show the 7 steps for hypothesis testing. (8 points)

c. Do the results in part (b) support or contradict the earlier research? Briefly explain. (3 points)

d.Give and interpret the p-value. (3 points)

e. What assumptions did you make regarding the populations? Use appropriate graphs to check the assumptions and give your supported conclusion. (3 points)