Question

In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in 2014, Felix Hernandez of the Seattle Mariners had the lowest ERA of any starting pitcher in the American League with an ERA of 2.14. In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was 0.721. In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was 0.762.

Question 1: Calculate the z-score for Clayton Kershaw. Round answer to 2 decimal places

Question 2: Calculate the z-score for Felix Hernandez. Round answer to 2 decimal places

Question 3: Which player had the better year relative to his peers? Explain using the z-scores you calculated

Answer 1

Z score is given by

1)

For National League

Mean, = 3.430

SD, = 0.721

Clayton Kershaw ERA, x = 1.77

Z score = (1.77- 3.430)/0.721 = -2.30

2)

For American League

Mean, = 3.598

SD, = 0.762

Felix Hernandez ERA, x = 2.14

Z score = (2.14- 3.598)/0.762 = -1.91

3)

Since Z score of Clayton is lower than that of Felix, Clayton had the better year as compared to his peers