Discuss the below:
Q: Team C is taken salaries from 15 randomly selected MLB teams in two conferences. At α = .05, is there a difference in the mean for all teams in the American League and National League? We think it is unlikely that there is a significant difference, but we will do a test of means to see whether our intuition is correct.
Major League Baseball Salaries for 2005 in Two Conferences
American League Salaries National League Salaries
Team Salaries Team Salaries
Boston 123.5 Philadelphia 95.5
NY Yankees 208.3 Washington 48.6
Baltimore 73.9 NY Mets 101.3
Toronto 45.7 Florida 60.4
Tampa Bay 29.7 Atlanta 86.5
Chicago Sox 75.2 St. Louis 92.1
Minnesota 56.2 LA Dodgers 83.0
Texas 55.8
X1 = 83.538 X2 = 81.057
S1 = 57.535 S2 = 19.382
N1 = 8 salaries N2 = 7 salaries
Step 1: Formulate the Hypotheses
To check for a significant difference without regard for its direction, we choose a two-tailed test. The hypotheses to be tested are
H0: μ1 = μ2
H1: μ1 _= μ2
Step 2: Calculate the Test Statistic