Refer to the Baseball 2010 data, which report information on the 30 Major League
ID: 2935236 • Letter: R
Question
Refer to the Baseball 2010 data, which report information on the 30 Major League Baseball teams for the 2010 season.
a) At the .05 significance level, can we conclude that there is a difference in the mean payroll of teams in the American League versus teams in the National League?
b) At the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American League versus teams in the National League?
c) Compute the mean and the standard deviation of the number of wins for the 10 teams with the highest payrolls. Do the same for the 10 teams with the lowest payrolls. At the .05 significance level, is there a difference in the mean number of wins for the two groups?
Show your work.
Explanation / Answer
b.
At the .05 significance level, can we conclude that there is a difference in the mean salary of teams in the American League versus teams in the National League? Data: x1 = 92.971 s1 = 39.2809 n1 = 14 x2 = 74.581 s2 = 25.7003 n2 = 16 Due to the sample sizes, the t-test must be used instead of the z-test. To determine which formula to use to calculate t(test), it is necessary to test the variances using the F-test. Test of Variances: Hypotheses: H0: s1 = s2 Ha: s1 s2 (Claim) Critical Value: At a = 0.05, with dfN = 15 and dfD = 13, F(crit) = 2.53 Test Value: F(test) = (s1)^2/(s2)^2 F(test) = (39.2809)^2 / (25.7003)^2 F(test) = 2.3361 Decision: F(test) < F(crit) --> Do not reject the null hypothesis Summary: There is not sufficient evidence to support the claim that the variances are different. Proceed to t-test for equal variances Hypotheses: H0: µ1 = µ2 Ha: µ1 µ2 (Claim) Critical Value: At a = 0.05, for a two-tailed test with 28 degrees of freedom, t(crit) = ± 2.048 Test Value: t(test) = (x1 - x2) / ( [ [ (n1 - 1)(s1)^2 + (n2 - 1)(s2)^2 ]/ (n1+ n2 - 2) ] [ ( 1/n1 +1/n2) ] ) t(test) = (92.971 - 74.581) / ( [ [ (14 - 1)(39.2809)^2 + (16 - 1)(25.7003)^2 ] / (14 + 16 - 2) ] [ ( 1/14 + 1/16) ] ) t(test) = 1.5361 Decision: t(test) < t(crit) --> Do not reject the null hypothesis Summary: There is not sufficient evidence to support the claim that there is a difference in the mean salary of teams in the American League versus teams in the National League.